Model-based control method, model-based control system, and storage medium

Abstract

This invention enables the temperature distribution of a temperature control component to more quickly approach a target temperature distribution. The model-based control method comprises steps a) to e). In step a), temperature control data is obtained, including temperature data for each region of the temperature control component installed in the processing device. In step b), for each region, the temperature of other regions is determined by a weighted average based on a weighting factor determined according to the magnitude of heat transfer between other regions. In step c), for each region, parameters of a multi-input single-output (MIMO) state-space model are determined using the determined temperatures of other regions and the temperature control data. In step d), a multi-input multiple-output (MIMO) state-space model is created by distributing the determined MIMO parameters to the elements of a multi-input multiple-output (MIMO) state-space model. In step e), the temperature of each region of the temperature control component is controlled using the MIMO state-space model.

Description

Model-based control methods, model-based control systems, programs This invention relates to a model-based control method, a model-based control system, and a program. In recent years, semiconductor manufacturing processes have demanded increasingly higher precision in miniaturization. A key aspect of this is the precise control of the temperature distribution on the substrate being processed during manufacturing. To achieve this precise temperature control, the stage on which the substrate is mounted is considered to be divided into multiple regions, with the temperature of each region controlled independently. However, if the number of independently controllable regions on the stage increases, the individual regions become smaller, making it difficult to install both heaters and temperature sensors in all regions. As a technique to avoid this situation, it is known to estimate the temperature of each region based on the relationship between the resistance value and temperature of heaters located in areas of the stage where the temperature can be independently controlled (for example, see Patent Document 1 below). The resistance value of the heater is calculated based on the measured values ​​of the voltage and current supplied to the heater. This eliminates the need to separately install temperature sensors in each region of the stage and the heaters, allowing for more independently controllable temperature zones to be installed on the stage. [Prior Art Documents] [Patent Documents] [Patent Document 1] Japanese Patent Application Publication No. 2021-9769 [The problem the invention aims to solve] This invention provides a technique that enables the temperature distribution of a temperature control component to more quickly approach a target temperature distribution. [Technical Means for Solving the Problem] One aspect of the model-based control method of the present invention includes steps a), b), c), d), and e). In step a), temperature control data is obtained, which includes temperature data of each region in a temperature control member disposed in a processing device and having multiple regions capable of individual temperature control. In step b), for each region, the temperature of other regions is determined by weighting an average of the temperatures of other regions based on a weighting factor determined according to the magnitude of heat transfer between other regions. In step c), for each region, parameters of a multi-input single-output (MIMO) state-space model are determined using the determined temperatures of other regions and the temperature control data. In step d), a multi-input multiple-output (MIMO) state-space model is created by distributing the determined parameters of the MIMO state-space model to the elements of a multi-input multiple-output (MIMO) state-space model. In step e), the temperature of each region of the temperature control member is controlled using the MIMO state-space model. [Effects of the Invention] According to the present invention, the temperature distribution of the temperature control component can be made to more quickly approach the target temperature distribution. The following description, with reference to the accompanying drawings, details the implementation of the model-based control method, model-based control system, and program disclosed herein. Furthermore, the disclosed model-based control method, model-based control system, and program are not limited by this implementation method. Furthermore, when controlling the temperature distribution of a platform with multiple independently controllable temperature zones, the power supplied to the heaters installed in each zone is controlled in such a way that the temperature of each zone becomes the target temperature. The power supplied to the heaters installed in each zone is mostly carried out through so-called PID (Proportional-Integral-Differential) control, which determines the control quantity based on the deviation between the control result and the target value. In PID control, as the deviation between the control result and the target value decreases as the control result approaches the target value, the control input decreases. Therefore, the time required until the control result stabilizes near the target value becomes longer. Furthermore, when controlling the temperature distribution of the control platform, the temperature of each area of ​​the platform is affected by the temperature of other areas. Therefore, if the power supplied to the heater is controlled solely based on the temperature of the area with the heater, the temperature of each area is not easily stabilized. Thus, the time required for the temperature of each area to approach the target value becomes longer. Therefore, the present invention provides a technique that enables the temperature distribution of temperature control components such as heaters to more quickly approach the target temperature distribution. (First Embodiment) [Configuration of Substrate Processing System 1] FIG1 is a system configuration diagram showing an example of the configuration of substrate processing system 1. Substrate processing system 1 includes substrate processing apparatus 10 and model data generation apparatus 20. Substrate processing apparatus 10 and model data generation apparatus 20 are connected via a communication network N such as LAN (Local Area Network). Substrate processing system 1 is an example of a model-based control system. The substrate processing apparatus 10 has a stage for placing a substrate. The stage has a plurality of regions. The temperature of each region can be individually controlled. Under various processing conditions, the substrate processing apparatus 10 measures the temperature data of each region of the stage on which the substrate is placed. Then, the measured temperature data of each region is transmitted as temperature control data to the model data generation apparatus 20 via the communication network N. Then, the substrate processing apparatus 10 receives the model data from the model data production apparatus 20 via the communication network N. The substrate processing apparatus 10 then uses the model data received from the model data production apparatus 20 to control the temperature of each area of ​​the stage. The substrate processing apparatus 10 then performs etching and other processes on the substrate placed on the stage. The model data creation apparatus 20 receives temperature control data from the substrate processing apparatus 10 via the communication network N, and uses the received temperature control data to create model data. The order of model data creation will be described below. Then, the model data creation apparatus 20 transmits the created model data to the substrate processing apparatus 10 via the communication network N. [Structure of Substrate Processing Apparatus 10] FIG2 is a schematic cross-sectional view showing an example of a substrate processing apparatus 10. In FIG2, as an example of a substrate processing apparatus 10, a capacitively coupled parallel plate plasma etching apparatus is shown. The substrate processing apparatus 10 includes a control device 100 and an apparatus body 110. The device body 110 includes, for example, a processing container 112 formed into a generally cylindrical shape using aluminum or the like. The surface of the processing container 112 is anodized. The processing container 112 is grounded. A stage 116 is provided inside the processing container 112. The stage 116 holds the substrate W on its upper surface and controls the temperature of the substrate W. Furthermore, in this embodiment, the substrate W is a generally circular substrate used to manufacture semiconductor devices, but the disclosed technology is not limited to this. As other forms, the substrate W may also be a rectangular plate or other shapes other than a generally circular plate. Also, as other forms, the substrate W may also be an FPD (Flat Panel Display) substrate or other substrate used to manufacture devices other than semiconductor devices. The stage 116 has an electrostatic chuck 118 and a base 120. A substrate W, which is to be processed, is placed on the upper surface of the electrostatic chuck 118. The base 120 is formed into a generally disc shape, for example, using a conductive material such as aluminum. The base 120 also functions as a lower electrode. The base 120 is supported by a support 114. The support 114 is a generally cylindrical component extending upward from the bottom of the processing container 112. At base station 120, an RF (Radio Frequency) power supply HFS is electrically connected via matching unit MU1. The RF power supply HFS generates RF power for plasma generation and supplies this RF power to base station 120. The frequency of the RF power for plasma generation is in the range of 27–100 MHz, and in one example, it is 40 MHz. Matching unit MU1 has circuitry for matching the output impedance of the RF power supply HFS with the input impedance of the load side (e.g., the base station 120 side). Furthermore, an RF power supply LFS is electrically connected to the base station 120 via a matching adapter MU2. The RF power supply LFS generates RF power (RF bias power) for feeding ions into the substrate W, and supplies the generated RF bias power to the base station 120. The frequency of the RF bias power is in the range of 400 kHz to 13.56 MHz, and in one example, it is a frequency of 3 MHz. The matching adapter MU2 has circuitry for matching the output impedance of the RF power supply LFS with the input impedance of the load side (e.g., the base station 120 side). An electrostatic chuck 118 is disposed on the base 120. The electrostatic chuck 118 uses electrostatic force to attract the substrate W, holding the substrate W on the upper surface of the electrostatic chuck 118. The electrostatic chuck 118 has an electrode E1 in its body, for example, formed of ceramic. The electrode E1 is electrically connected to a DC power supply 122 via a switch SW1. The DC voltage supplied from the DC power supply 122 causes an electrostatic force to be generated on the surface of the electrostatic chuck 118 by the electrode E1. An annular edge ring ER is disposed on the upper surface of the substrate 120 and around the electrostatic chuck 118, in a manner that surrounds the substrate W. The edge ring ER improves the uniformity of plasma processing on the substrate W. The edge ring ER is formed of a material appropriately selected according to the plasma processing to be performed, such as silicon or quartz. The edge ring ER is also sometimes referred to as a focusing ring. Furthermore, a plurality of heaters HT are provided on the electrostatic chuck 118. In this embodiment, the upper surface of the electrostatic chuck 118 is divided into a plurality of regions Z, for example, as shown in FIG3. In the example of FIG3, the upper surface of the electrostatic chuck 118 is divided into 15 regions Z, for example. Moreover, the number of regions Z is not limited to 15; it may be more or less than 15. Furthermore, the method of dividing the regions Z is not limited to the example of FIG3; it may also be a grid-like, concentric circle, radial, or combination thereof division method. In this embodiment, one heater HT is provided for each region Z. Alternatively, two or more heaters HT may be provided for each region Z, and the number of heaters HT may vary between regions Z. In this embodiment, a heater HT is also provided on the lower surface of the edge ring ER. That is, in this embodiment, a total of 16 heaters HT are provided on the electrostatic chuck 118 and the edge ring ER. Furthermore, in this embodiment, the edge ring ER is also treated as one region Z. Therefore, in this embodiment, a total of 16 regions Z are provided on the electrostatic chuck 118 and the edge ring ER. The electrostatic chuck 118 and the edge ring ER are examples of temperature control components. Furthermore, in this embodiment, the temperature control component is an electrostatic chuck 118 that has multiple regions capable of individually controlling the temperature and controlling the temperature distribution of the substrate W, but the disclosed technology is not limited to this. The temperature control component can be any component other than the electrostatic chuck 118, as long as it has multiple regions capable of individually controlling the temperature. A heater control circuit 160 is connected to each heater HT. Each heater HT heats up by power individually supplied from the heater control circuit 160, and heats the corresponding area Z. Figure 4 is a diagram showing an example of the heater control circuit 160. The heater control circuit 160 has a plurality of control blocks 161-1 to 161-n and a measuring unit 165. Furthermore, hereinafter, when referring to the plurality of control blocks 161-1 to 161-n collectively without distinguishing them, it will be referred to as control block 161. Control block 161 is equipped with one heater HT for each of the areas Z, and supplies power to the corresponding heater HT. Control block 161 includes ammeter 163, voltmeter 164, and switch SW2. Switch SW2 is turned on and off according to control from control device 100. This adjusts the power supplied from power source 166 to the corresponding heater HT according to the operating ratio of switch SW2 being on and off. Ammeter 163 measures the current supplied from power source 166 to the corresponding heater HT and outputs the measured current value to measuring unit 165. Voltmeter 164 measures the voltage supplied from power source 166 to the corresponding heater HT and outputs the measured voltage value to measuring unit 165. The measuring unit 165 measures the resistance value of each heater HT based on the measured values ​​of current and voltage output from each control block 161. Then, the measuring unit 165 outputs the measured resistance value data of each heater HT to the control device 100. Returning to Figure 2 for further explanation. A flow path 124 is formed inside the base 120. Refrigerant is supplied to the flow path 124 via piping 126a from a cooler unit (not shown) located outside the processing container 112. The refrigerant supplied to the flow path 124 returns to the cooler unit via piping 126b. The temperature of the refrigerant is controlled by the cooler unit. An upper electrode 130 is provided inside the processing container 112. The upper electrode 130 is positioned above the stage 116 and faces the base 120. In this embodiment, the base 120 and the upper electrode 130 are arranged in a manner that is substantially parallel to each other. The upper electrode 130 is supported on the upper part of the processing container 112 via an insulating shielding member 132. The upper electrode 130 includes an electrode plate 134 and a support 136. The electrode plate 134 faces the processing space S between the stage 116 and the upper electrode 130, and has a plurality of gas outlets 134a. The electrode plate 134 may be made of a low-resistance conductor or semiconductor with low Joule heating. The support body 136 is formed of a conductive material such as aluminum and supports the electrode plate 134 detachably from above. The support body 136 may also have a water-cooling structure. A gas diffusion chamber 136a is provided inside the support body 136. A plurality of gas inlets 136b, connected to the gas outlet 134a, extend downward from the gas diffusion chamber 136a. Furthermore, a gas inlet 136c is provided in the support body 136 to introduce gas into the gas diffusion chamber 136a. A pipe 138 is connected to the gas inlet 136c. A gas source group 140 is connected to piping 138 via a valve group 142 and a flow controller group 144. The valve group 142 has a plurality of on / off valves. The flow controller group 144 has a plurality of flow controllers, including a mass flow controller. The gas source group 140 has gas sources for a plurality of gases required for plasma processing. The plurality of gas sources in the gas source group 140 are connected to piping 138 via corresponding on / off valves and corresponding mass flow controllers. In the substrate processing apparatus 10 illustrated in Figure 2, one or more gases from one or more gas sources selected from the plurality of gas sources in the gas source group 140 are supplied to the piping 138. The gas supplied to the piping 138 diffuses in the gas diffusion chamber 136a and is ejected in a burst shape into the processing space S through the gas flow port 136b and the gas ejection port 134a. A grounding conductor 112a is provided above the upper electrode 130 in a manner that covers the upper electrode 130. The grounding conductor 112a is formed into a generally cylindrical shape by means of metal and is grounded through the processing container 112. An accumulation cover 146 is detachably mounted and detachably disposed along the inner wall of the processing container 112. The accumulation cover 146 is also disposed on the outer periphery of the support portion 114. The accumulation cover 146 is, for example, constructed by covering an aluminum material with a Y-shaped structure. 2O It is formed of grade 3 ceramic to prevent etching byproducts (so-called deposits) from adhering to the inner wall of the processing container 112. On the bottom side of the processing container 112, between the support 114 and the inner wall of the processing container 112, for example, a Y-shaped structure is provided due to the aluminum coating. 2O An exhaust plate 148 is formed of grade 3 ceramic. An exhaust port 112e is provided below the exhaust plate 148. An exhaust device 150 is connected to the exhaust port 112e via an exhaust pipe 152. The exhaust device 150 has a vacuum pump such as a turbomolecular pump, which can reduce the pressure inside the processing container 112 to the desired vacuum level. Furthermore, an opening 112g is formed on the side wall of the processing container 112 for loading and unloading the substrate W. The opening 112g is opened and closed by a gate valve 154. The device body 110 configured as described above is controlled in a comprehensive manner by a control device 100 configured as shown in FIG. 5. The control device 100 is implemented, for example, by a computer. FIG. 5 is a diagram showing an example of the control device 100 included in the substrate processing apparatus 10 of the first embodiment. The control device 100 includes a communication I / F (interface) 101, a user I / F 102, a control unit 103, and a memory unit 104. The control unit 103 is an example of a second control unit. Communication I / F 101 communicates with the device body 110. Furthermore, communication I / F 101 communicates with the model data fabrication device 20 via the communication network N. User I / F 102 provides an interface for the user of the substrate processing device 10 to operate the substrate processing device 10. The memory unit 104 includes RAM (Random Access Memory), ROM (Read Only Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), or a combination thereof. The memory unit 104 stores a correspondence table 1040, model data 1041, and process recipe 1042. The correspondence table 1040 shows the relationship between the resistance value of the heater HT and its temperature. The model data 1041 shows data representing the temperature changes of the heater HT in each region Z, fabricated using the model data fabrication device 20. The process recipe 1042 includes data such as the processing conditions of the substrate W. In addition to these, the memory unit 104 also stores programs. The control unit 103 has a processor such as a CPU (Central Processing Unit) or a DSP (Digital Signal Processor). The control unit 103 executes the programs stored in the memory unit 104 to realize the functions of the data collection unit 1030, the temperature control unit 1031, and the process recipe execution unit 1032. The data collection unit 1030 controls the device body 110 according to instructions from the model data production device 20, and collects data on the resistance values ​​of the heaters HT installed in each region Z under multiple processing conditions. The multiple processing conditions are, for example, temperature control condition data as shown in Figure 6A. Figure 6A is a diagram illustrating an example of temperature control condition data. The temperature control condition data illustrated in Figure 6A includes the initial temperature of each region, the set temperature of each region, the power supply voltage of the power supply 166 supplying power to the heaters HT in the corresponding region, and the temperature of the refrigerant controlled by the cooler unit (cooler temperature), etc. In the temperature control condition data illustrated in Figure 6A, n represents the number of regions, m represents the number of temperature control conditions, and SP (Set Point) represents the set value or target value. Then, the data collection unit 1030 refers to the correspondence table 1040 in the memory unit 104 and specifies the temperature corresponding to the collected resistance value. Then, for each processing condition, the data collection unit 1030 generates temperature control data containing temperature data for each region Z. For example, in the case of PID control performed to obtain data for modeling, control is performed while feeding back resistance to convert temperature. Specifically, the resistance value is converted to temperature, and the operating quantity is determined based on the deviation between that temperature and a reference value. Furthermore, when data is obtained by inputting a predetermined operating quantity such as a pulse response or step response, it is also possible to collect only the resistance value and then convert it to temperature. Furthermore, the temperature of each region Z can also be obtained via the substrate W placed on the electrostatic chuck 118. The temperature distribution of the substrate W placed on the electrostatic chuck 118 can be measured, for example, by using a temperature sensor such as an infrared or fiber optic sensor. By measuring the temperature distribution of the substrate W, the temperature of region Z corresponding to the region of the substrate W can be estimated. Figure 6B is a diagram illustrating an example of temperature control data. In the temperature control data illustrated in Figure 6B, a correspondence is established between the temperature of each region Z, the operating parameters of each region, the power supply voltage, and the cooler temperature. Then, the data collection unit 1030 transmits the generated temperature control data to the model data generation device 20 via the communication I / F 101. When the temperature control unit 1031 receives model data from the model data generation device 20, it stores the received model data in the memory unit 104. Furthermore, when the process recipe execution unit 1032 executes the process recipe 1042, the temperature control unit 1031 uses the model data 1041 to specify the power supplied to the heaters HT installed in each region Z. Then, the temperature control unit 1031 controls the switch SW2 of the corresponding heater control circuit 160 to supply the specified power to each heater HT. The process recipe execution unit 1032 controls each part of the device body 110 based on the process recipe 1042 to perform processing on the substrate W. [Composition of Model Data Creation Apparatus 20] Figure 7 shows an example of a model data creation apparatus 20. The model data creation apparatus 20 is implemented, for example, by a computer. The model data creation apparatus 20 includes a communication I / F 21, a user I / F 22, a control unit 23, and a memory unit 24. The control unit 23 is an example of a first control unit. The communication I / F 21 is an example of an output unit. Communication I / F21 communicates with the substrate processing device 10 via communication network N. User I / F22 provides an interface for users of the model data creation device 20 to operate the model data creation device 20. The memory unit 24 includes RAM, ROM, HDD, SSD, or a combination thereof. Temperature control data 240 and weighting factors 241 are stored in the memory unit 24. The temperature control data 240 includes data on the temperature of each region Z measured under various conditions in the substrate processing apparatus 10. The weighting factors 241 are used for generating model data. Details of the weighting factors 241 will be described below. In addition, programs are also stored in the memory unit 24. The control unit 23 has a processor such as a CPU or DSP. The control unit 23 performs the functions of the data collection unit 230 and the model data generation unit 231 by executing the program stored in the memory unit 24. The data collection unit 230 instructs the substrate processing apparatus 10 to generate temperature control data via the communication I / F 21. Then, it receives the temperature control data from the substrate processing apparatus 10 via the communication I / F 21 and stores the received temperature control data in the memory unit 24. The model data generation unit 231, referencing the temperature control data 240 and weighting factor 241, generates model data that models the temperature changes of a plurality of heaters HT. Then, the model data generation unit 231 transmits the generated model data to the substrate processing device 10 via communication I / F 21. [Processing of Model Data Generation Apparatus 20] Figure 8 is a flowchart illustrating an example of the processing of the model data generation apparatus 20. The processing illustrated in Figure 8 is achieved by the control unit 23 reading the program from the memory unit 24 and executing the read program. The processing shown in Figure 8 and Figure 10 below is an example of a model-based control method. First, the data collection unit 230 instructs the substrate processing apparatus 10 to collect temperature control data and receives the temperature control data from the substrate processing apparatus 10 (S100). Then, the data collection unit 230 stores the received temperature control data in the memory unit 24. Step S100 is an example of process a). Next, the model data production unit 231 initializes the value of variable i to 1 (S101). Then, the i-th region Z is selected (S102). Then, the model data production unit 231 calculates the weighted average temperature of regions Z other than the i-th region Z (S103). Step S103 is an example of process b). Here, in this embodiment, the temperature of each region Z is represented by a discretized state equation. Hereinafter, as an example of a discretized state equation, the case of using an ARX (Auto-Regressive eXogenous) model will be explained. Hereinafter, there are cases where the data of the ARX model is recorded as model data. The ARX model is an example of a regression model. Furthermore, a regression model is an example of a state-space model with (specific) multiple-input, single-output parameters, and the coefficients of the regression model are an example of the parameters of a multiple-input, single-output state-space model. The temperature x(t) of each region Z is represented using an ARX model, for example, as shown in equation (1) below. [Equation 1] In equation (1) above, x i (t) represents the temperature of the i-th region Z. i(t) represents the operating amount of power supplied to the heater HT in the i-th region Z. v(t) represents the magnitude of the power supply voltage supplied to the heater HT in each region Z. z(t) represents the temperature of the refrigerant supplied from the cooler unit (not shown) to the flow path 124 inside the base 120. a i Let b represent the autoregressive coefficient of the i-th region Z. i c represents the temperature coefficient of region Z, which is different from the i-th region Z. i d represents the coefficient representing the operating amount of electricity supplied to the heater HT in the i-th region Z. i e represents the coefficient of the cross term between the power supply voltage and the operating quantity of the heater HT supplied to the i-th region Z. i f represents the coefficient of temperature of the refrigerant that affects the i-th region Z. i This represents a constant term relative to the i-th region Z. In step S103, the term expressed in equation (2) above is used as the weighted average of the temperatures of regions Z other than the i-th region Z. [Number 2] In equation (2) above, w ij The magnitude of heat transfer between the i-th region Z and the j-th region Z, which is different from the i-th region Z, is represented by a positive weighting factor that sums to 1. In this embodiment, the weighting factor w is determined based on the area of ​​the boundary surface between adjacent regions Z. Specifically, for example, as shown in Figure 9, when the 2nd to 4th regions Z2 to Z4 are adjacent to the 1st region Z1, and the area of ​​the boundary surface between region Z1 and regions Z2 to Z4 is the same, the weighting factor w... ij Become w 12 =w 13 =w 14 =1 / 3. Furthermore, in the example of Figure 9, this is based on the premise that regions Z1 to Z4 have the same material. Also, when the thickness of the boundary surfaces of regions Z1 and Z2 to Z4 is the same, the weighting factor w... 12 w 13 and w 14The length of the boundary in the face direction of the electrostatic chuck 118 of region Z1 and the second to fourth regions Z corresponds to the length of the boundary in the face direction of region Z1. In this embodiment, the weighting factor w is considered to be 0 for non-adjacent regions Z. This reduces the computational load on the model data generation unit 231. Furthermore, if the configuration of each region Z is determined, the weighting factor w... ij The weighting factor w is determined uniquely. Therefore, in this embodiment, before performing the process illustrated in Figure 8, the weighting factor w is determined. ij It is pre-calculated and stored in memory unit 24. Furthermore, in this embodiment, the sum of the weighting factors w is a positive value of 1. This suppresses the effects of multicollinearity when identifying coefficients in the regression model, allowing for accurate identification of the coefficients in the regression model. Secondly, the model data production unit 231 specifies the coefficients a of the ARX model represented by (1) above. i ~f i (S104). Step S104 is an example of process c). In step S104, temperature control data is used to train an ARX model using a regression algorithm, and the coefficients a of the ARX model are identified. i ~f i The coefficients of the regression model are specified using regression algorithms such as OLS (Ordinary Least Squares regression), Lasso, Ridge, or ElasticNet. Secondly, the model data production department 231, based on the weighting factor w ij Let the coefficient b i Distribute the data to all regions Z except the i-th region (S105). In step S105, the coefficient b allocated to the j-th region Z is... i Become b i w ij . Secondly, the model data production unit 231 will calculate the weighting factor w. ij The coefficient b allocated to each region Z other than the i-th region iAdd elements to the matrix (S106). Steps S105 and S106 are examples of process d). Then, the model data production unit 231 determines whether the value of variable i reaches the value of constant n representing the quantity of region Z (S107). If the value of variable i does not reach the value of constant n (S107: No), the model data production unit 231 increases the value of variable i by 1 (S108) and executes the process shown in step S102 again. On the other hand, when the value of variable i reaches the value of constant n (S107: Yes), the model data generation unit 231 sends the model data, which includes the matrix of elements added in step S106, to the substrate processing device 10 via communication I / F21 (S109). Then, the model data generation device 20 ends the processing shown in this flowchart. The model data sent to the substrate processing apparatus 10 in step S109 is represented, for example, by the following formula (3). The model data in this embodiment is an example of a multiple-input multiple-output state-space model. [3] In equation (3) above, the matrix x(t+1) is represented, for example, in equation (4) below. [Equation 4] Furthermore, in equation (3) above, matrix A can be represented, for example, as in equation (5) below. [Equation 5] Furthermore, in equation (3) above, matrix B can be represented, for example, as in equation (6) below. [Equation 6] Furthermore, in equation (3) above, matrix C is represented, for example, in equation (7) below. [Number 7] [Processing of the substrate processing apparatus 10] FIG10 is a flowchart illustrating an example of the processing of the substrate processing apparatus 10. The processing illustrated in FIG10 is achieved by the control unit 103 of the control device 100 reading the program from the memory unit 104 and executing the read program. The processing illustrated in FIG10 is an example of process e). First, the data collection unit 1030 determines whether the model data generation device 20 has instructed the generation of temperature control data via the communication I / F 101 (S200). If the generation of temperature control data has been instructed (S200: Yes), the data collection unit 1030 sets processing conditions and measures the temperature of each region Z (S201). In step S201, the data collection unit 1030 controls the device body 110 to collect data on the resistance values ​​of the heaters HT installed in each region Z under multiple processing conditions. Then, the data collection unit 1030 refers to the correspondence table 1040 in the memory unit 104 and identifies the temperature corresponding to the collected resistance value. Then, for each processing condition, the data collection unit 1030 generates temperature control data containing data on the temperature of each region Z. Next, the data collection unit 1030 sends the temperature control data generated in step S201 to the model data generation device 20 via the communication I / F 101 (S202). Then, the process shown in step S200 is executed again. On the other hand, when no instruction is given to generate temperature control data (S200: No), the temperature control unit 1031 determines whether model data has been received from the model data generation device 20 via the communication I / F 101 (S203). If model data has been received (S203: Yes), the temperature control unit 1031 stores the received model data in the memory unit 104 (S204). Then, the process described in step S200 is executed again. On the other hand, if no model data is received (S203: No), the temperature control unit 1031 and the process recipe execution unit 1032 determine whether the user of the substrate processing device 10 has instructed the execution of the process recipe via the user I / F 102 (S205). If the execution of the process recipe is instructed (S205: Yes), the temperature control unit 1031 uses the model data 1041 in the memory unit 104 to specify the power supplied to the heaters HT installed in each region Z as the operating quantity (S206). In step S206, the temperature control unit 1031 specifies the temperature of each region Z that is the temperature distribution specified by the process formula 1042 in the memory unit 104. Then, the temperature control unit 1031 uses the specified temperature as the target value and the model data 1041 in the memory unit 104 to specify the power supplied to the heater HT of each region Z as the operating quantity. The temperature control unit 1031 uses the model data 1041 to specify the power supplied to the heater HT of each region Z, for example, by means of an optimal control factor or model predictive control. Then, the temperature control unit 1031 controls the switch SW2 of the corresponding heater control circuit 160 for each heater HT in such a way as to supply the specified power. Next, the process formula execution unit 1032 controls each part of the device body 110 to perform the processing of the substrate W according to the process formula 1042 (S207). On the other hand, if no process recipe execution is instructed (S205: No), the process recipe execution unit 1032 determines whether to terminate the process (S208). If the process is not terminated (S208: No), the process shown in step S200 is executed again. On the other hand, if the process is terminated via user I / F102 through instructions from the user or others from the substrate processing device 10 (S208: Yes), the process shown in this flowchart is terminated. [Simulation Results] Here, the advantages of the temperature control method in this embodiment will be explained. Figure 11 is a diagram showing an example of the temperature changes in each region Z during temperature control in the comparative example. In the comparative example, the power supplied to the heater HT in each region Z is controlled by PID control. Figure 11 shows the temperature changes in four regions (Z1, Z6, Z10, and Z13) among the plurality of regions Z, where the temperature difference is relatively large as shown in Figure 12. In the example of Figure 11, control is performed such that the temperature of each region Z is 90°C. As shown in Figure 11, when the temperature of each region Z is individually controlled by PID control, the temperature of each region Z has not yet stabilized sufficiently within 200 msec from the start of control. Furthermore, in the comparative example of Figure 11, the difference in the rate of temperature change of each region Z is also relatively large during the temperature change process, resulting in a larger temperature difference between regions Z. Therefore, when processing of substrate W begins before its temperature stabilizes at the target temperature, the uneven temperature distribution of substrate W leads to a decrease in the uniformity of substrate W processing. In contrast, when using the model-based temperature control method of this embodiment, the temperature change of each region Z is, for example, as shown in Figure 13. Figure 13 is a diagram showing an example of the temperature change of each region Z in the temperature control of this embodiment. In Figure 13, the temperature changes of the four regions (Z1, Z6, Z10, and Z13) shown in Figure 12 are also shown, but since the temperature changes of each region Z are roughly the same, the trajectories of the temperature changes largely overlap. As shown in Figure 13, when the temperature of each region Z is controlled at 4°C / sec using the model-based control in this embodiment, the temperature of each region Z can be sufficiently stabilized at the target temperature within 200 msec from the start of control. Therefore, according to the temperature control method of this embodiment, the temperature distribution of the electrostatic chuck 118 and the edge ring ER can more quickly approach the target temperature distribution. Furthermore, in the example of Figure 13, during the temperature change of each region Z, the difference in the rate of temperature change of each region Z is also small, and the temperature difference between each region Z becomes smaller. Therefore, even if the processing of the substrate W begins during the period until the temperature of the substrate W stabilizes at the target temperature, the unevenness of the temperature distribution of the substrate W is also small, and the uniformity of the processing of the substrate W can be improved. Moreover, as shown in Figure 13, by finely specifying the temperature intermediate to reach the final target temperature as the target temperature, temperature changes with arbitrary slopes such as 3°C / sec and 2°C / sec can also be achieved. The first embodiment has been described above. As described above, the model-based control method in this embodiment includes steps a), b), c), d), and e). In step a), temperature control data is obtained, which includes temperature data of each region Z in a temperature control member provided in the substrate processing apparatus 10 and having a plurality of regions Z that can be individually controlled. In step b), for each region Z, the temperature of other regions Z is determined by weighting a factor w determined based on the magnitude of heat transfer between other regions Z. In step c), for each region Z, parameters of a multi-input single-output state-space model are determined using the determined temperatures of other regions and the temperature control data. In step d), model data is generated by allocating the determined parameters of the multi-input single-output state-space model to elements of model data, which is an example of a multi-input multi-output state-space model. In step e), the model data is used to control the temperature of each region Z of the temperature control member. This allows the temperature distribution of the temperature control components to more quickly approach the target temperature distribution. Here, when controlling the temperature distribution of the stage, the temperature of each region of the stage is affected by the temperature of other regions. Therefore, when considering the thermal interference effect of the estimated temperature of each region on the temperature of adjacent regions, a large amount of experimental data for temperature control is required, which is impractical. In contrast, in the model-based control method of this embodiment, a regression model is used to estimate the temperature of each region, so even with a smaller amount of experimental data, the temperature of each region can be controlled with good accuracy. Furthermore, in the above embodiment, the weighting factor w of each region Z is determined based on the area or length of its boundary with other adjacent regions Z, and the weighting factor w relative to other non-adjacent regions Z is 0. Here, as the number of regions increases, the number of parameters that can be included in the explanatory variables increases, but parameters that are unrelated to each other must be excluded. In the above embodiment, by making the weighting factor w relative to other non-adjacent regions Z 0, the number of explanatory variables can be reduced. This reduces the computational load when generating model data. Furthermore, in the above embodiment, the temperature control member is a stage 116 for placing the substrate W and controlling the temperature of the substrate W. This allows the temperature distribution of the substrate W during processing to more quickly approach the target temperature distribution. Furthermore, in the above embodiments, the multi-input multi-output state-space model includes a term representing the temperature of the refrigerant controlled by the cooler unit cooling multiple regions Z, and a term representing the magnitude of the power supply voltage supplied to the heater HT heating multiple regions Z. Therefore, even when there are changes in the refrigerant temperature and power supply voltage, reproducible control can be performed, and control can be performed according to a specified temperature change trajectory. Furthermore, in the above embodiments, the multi-input single-output state-space model is an ARX model. This allows for a well-accurate modeling of the state of a temperature control component with multiple regions Z. Furthermore, in the above embodiments, the parameters of the multi-input single-output state-space model are specified using OLS, Lasso, Ridge, or Elastic Net. This allows for the accurate specification of the regression model coefficients. In particular, by using Lasso, Ridge, or Elastic Net, overlearning can be suppressed. Furthermore, in the above embodiments, at least one of the plurality of regions differs from its adjacent regions in at least one aspect: the shape of the region, the shape of its boundary surface, or its material. If the adjacent states of adjacent regions differ, the weighting factors between adjacent regions will also differ, making it more difficult to prepare experimental data. In contrast, in this embodiment, by using a multi-input multi-output state-space model, even if the adjacent states of adjacent regions differ, the temperature of the plurality of regions can be accurately estimated with less experimental data. Furthermore, in the above embodiments, the temperature control data, including the temperature of each region, is obtained via a substrate placed on the temperature control member. Furthermore, in the above embodiments, the weighting factors sum to a positive value of 1. Here, when modeling using data from multiple regions simultaneously controlled by temperature, the high correlation between regions leads to multicollinearity, causing the model coefficients to be incorrectly determined. In contrast, the model-based control method in this embodiment uses weighting factors that sum to a positive value of 1 for modeling. This suppresses excessively high correlations between temperature-related regions Z, thus mitigating the effects of multicollinearity. Furthermore, the substrate processing system 1 in the above embodiment is a model-based control system, and includes a substrate processing apparatus 10 and a model data generation apparatus 20. The model data generation apparatus 20 has a control unit 23 configured to generate a state space model, and a communication I / F 21 configured to output the state space model to the substrate processing apparatus 10. The substrate processing apparatus 10 has a temperature control member configured to have a plurality of regions Z capable of individual temperature control, a memory unit 104 configured to acquire and store the state space model generated by the model data generation apparatus 20, and a control unit 103 configured to use the state space model stored in the memory unit 104 to control the temperature of each region Z of the temperature control member. The control unit 23 of the model data generation apparatus 20 executes steps a), b), c), and d). In step a), temperature control data including data on the temperature of each region Z measured in the temperature control member is acquired. In step b), for each region Z, a weighted average temperature of the other regions Z is determined using a positive weighting factor w, which is determined based on the magnitude of heat transfer between the region Z and other regions Z, and whose sum is 1. In step c), for each region Z, a regression model using the determined temperatures of the other regions is trained using temperature control data, and the coefficients of the regression model are determined. In step d), model data is created by allocating the coefficients of the determined regression model to the elements of the model data, which is an example of a multi-input multi-output state-space model. By creating the model data and using it for model-based control, higher control performance is achieved. In this way, the substrate processing apparatus 10 can make the temperature distribution of the temperature control component more quickly approach the target temperature distribution. Furthermore, the program in the above embodiment causes the computer to execute processes a), b), c), and d). In process a), temperature control data is obtained, which includes temperature data of each region Z measured in a temperature control member disposed on the substrate processing device 10 and having a plurality of regions Z capable of individual temperature control. In process b), for each region Z, a weighted average temperature of other regions Z is determined using a positive weighting factor w determined based on the magnitude of heat transfer between other regions Z and summed to 1. In process c), for each region Z, a regression model using the determined temperatures of other regions is trained using the temperature control data, and the coefficients of the regression model are determined. In process d), model data is generated by distributing the determined coefficients of the regression model to the elements of model data, which is an example of a multi-input multi-output state-space model. The substrate processing apparatus 10 controls the temperature distribution of the temperature control component by using model data generated by a computer, which enables the temperature distribution of the temperature control component to more quickly approach the target temperature distribution. (Second Embodiment) In the second embodiment, during the use of the substrate processing apparatus 10, the temperature distribution of each region Z after temperature control using model data is measured, and the coefficients of the model data are updated based on the measurement results. By correcting the model data according to the actual characteristics of the substrate processing apparatus 10, the accuracy of temperature control can be improved. Furthermore, since the coefficients of the model data are corrected to follow the changes in the substrate processing apparatus 10 over time due to component consumption, the deterioration in the accuracy of temperature distribution control in each region Z that occurs over time with the substrate processing apparatus 10 can be minimized. Hereinafter, the differences from the first embodiment will be described. Figure 14 is a diagram showing an example of the control device 100 included in the substrate processing apparatus 10 of the second embodiment. In this embodiment, the control unit 103 executes a program stored in the memory unit 104, thereby realizing the function of the model data update unit 1033. The model data update unit 1033 updates the coefficients of the model data through adaptive control. Adaptive control refers to the control that updates the model based on the residual between the predicted value and the measured value during actual machine operation, thereby eliminating model errors. Figure 15 is a diagram illustrating an example of the update order of coefficients in the model data. First, the process recipe execution unit 1032 outputs the target temperature specified by the process recipe 1042 stored in the memory unit 104 to the temperature control unit 1031. The temperature control unit 1031 uses the model data 1041 stored in the memory unit 104 to specify the power supplied to the heaters HT in each region Z as the operating quantity. Then, the temperature control unit 1031 controls the switch SW2 of the heater control circuit 160 for each heater HT according to the specified operating quantity. The temperature control unit 1031 outputs the predicted temperature value for each region Z relative to the operating quantity to the model data update unit 1033. The model data update unit 1033 collects the resistance values ​​of the heaters HT in each region Z. Then, the model data update unit 1033 refers to the correspondence table 1040 in the memory unit 104 and specifies the temperature corresponding to the resistance values ​​collected for each region Z as the measured value. The process of specifying the measured temperature for each region Z is an example of process f). Then, for each region Z, the model data update unit 1033 calculates the difference between the specified measured value and the predicted value output from the temperature control unit 1031 as the prediction error. Then, the model data update unit 1033 specifies the coefficients of the updated model data, for example, using the following equations (8) to (11). [Equation 8] [Number 9] [Number 10] [Number 11] The definitions of the symbols shown in equations (8) to (11) above are as follows. [Number 12] y: measured value Predicted value : Regression vector (measured values, power supply voltage, cooler temperature) λ: Forgetting coefficient Model data coefficients (ARX model coefficients) K: Adaptation gain P: Variance-covariance matrix Then, the model data update unit 1033 updates the coefficients of the model data 1041 in the memory unit 104 with the specified coefficients. The process of updating the coefficients of the model data 1041 is an example of process g). The temperature control unit 1031 uses the updated model data 1041 to specify the power supplied to the heaters HT in each region Z. [Experimental Results] Figure 16 illustrates one example of the effect of adaptive control. Similar to the simulations in Figures 11 and 13, Figure 16 shows the temperature changes in four regions (Z1, Z6, Z10, and Z13: refer to Figure 12) where the temperature difference between regions Z is relatively large. As shown in Figure 16, by implementing adaptive control, the temperature difference between regions Z can be suppressed to less than ±0.2℃ compared to the case without adaptive control. This improves the accuracy of temperature distribution control. [Application of Model Data Using Application Control] Figure 17 is a flowchart illustrating an example of the application sequence of model data using application control. First, reference model data is generated using temperature control data from a plurality of substrate processing devices 10 that serve as references (S300). Secondly, in the mass production process of the substrate processing apparatus 10, before shipment, the reference model data is used for experimental application, and the reference model data is updated by adaptive control (S301). Next, the updated baseline model data is stored as individual model data in the memory unit 104 of the substrate processing device 10 before shipment (S302). Next, after the substrate processing apparatus 10 is shipped, individual model data is used in the manufacturing process of substrate W, and the individual model data is updated by adaptive control (S303). In step S303, the individual model data before the update is stored in the memory unit 104, separated from the updated individual model data. Then, when the use of the substrate processing apparatus 10 is terminated, the updated individual model data is discarded (S304). Then, when the use of the substrate processing apparatus 10 is restarted, the process shown in step S303 is executed again. Thus, in this embodiment, each time the application ends, the updated individual model data is returned to the individual model data saved at the time of shipment. This prevents performance degradation when significant temperature changes occur again, by using adaptive control to adapt to the previous temperature setting. Furthermore, to accommodate component consumption, an adaptive control program is executed to update the individual model data. The second embodiment has been described above. As described above, the model-based control method in this embodiment further includes steps f) and g). In step f), temperature data of each region Z measured during the operation of the substrate processing apparatus 10 are obtained. In step g), based on the error between the temperature predicted using the state-space model and the temperature obtained in step f), the coefficients of each element of the state-space model are updated by adaptive control. This reduces the error between the behavior of the actual temperature control components (electrostatic chuck 118 and edge ring ER) and the behavior of the multi-input multi-output state-space model. This reduces the impact of model errors due to individual differences in the temperature control components. Furthermore, it enables model updates for errors in actual operation. (Third Embodiment) In the first and second embodiments described above, each region Z of the temperature control member is made of the same material. In contrast, in this embodiment, when there is a region Z of a material different from that of other regions Z within the region Z of the temperature control member, the ARX model is represented by a weighted factor w based on the magnitude of heat conduction between regions Z of different materials. For example, as shown in Figure 18, consider regions Z1 to Z3 with thermal conductivity λ A Material A is formed, and region Z4 is composed of material with thermal conductivity λ. B The formation of material B. In the example of Figure 18, regions Z2 to Z4 are adjacent to region Z1, and the area of ​​the boundary surface of region Z1 is the same as that of regions Z2 to Z4. Also, in the example of Figure 18, the thickness of the boundary surface of region Z1 is the same as that of regions Z2 to Z4. If the materials of regions Z1 to Z4 are the same, then they become the weighting factor w. 12 =w 13 =w 14 =1 / 3, but since the materials of regions Z1 to Z3 are different from those of region Z4, the weighting factor is adjusted as shown in equation (13) below. [Equation 13] The third embodiment has been described above. As mentioned above, in the model-based control method of this embodiment, the weighting factor of each region Z is determined based on the magnitude of heat conduction caused by the difference between the material of region Z and the material of other adjacent regions Z. Therefore, even when the region Z of the temperature control member includes regions Z with materials different from those of other regions Z, weighting based on the actual magnitude of heat conduction between regions Z can be assigned. [Other] Furthermore, the technology disclosed in this case is not limited to the above-described embodiments and various changes can be made within the scope of its intent. For example, in the embodiments described above, a weighting factor w is defined between adjacent regions Z, and the weighting factor w is considered to be 0 between non-adjacent regions Z. However, the disclosed technology is not limited to this. As another form, a weighting factor w can also be assigned between non-adjacent regions Z. The weighting factor between non-adjacent regions Z can also be determined by considering, for example, the distance between regions Z and the material of the components interposed between regions Z. Furthermore, in the above embodiments, each region Z is provided with one heater HT, and the temperature of the corresponding region Z is estimated based on the resistance value of the heater HT; however, the disclosed technology is not limited to this. Alternatively, each region Z may be provided with a temperature sensor for measuring the temperature of region Z. In this case, the distance between the temperature measurement point of region Z and other regions, and the distance between the temperature measurement point of region Z and the heating point where the heater HT is located, can be weighted and incorporated into the model data. Furthermore, when multiple temperature sensors are provided for each region Z, for each measurement point, the distance between the temperature measurement point of region Z and other regions, and the distance between the temperature measurement point of region Z and the heating point where the heater HT is located, can also be weighted and incorporated into the model data. Furthermore, in the above embodiments, the electrostatic chuck 118 and the edge ring ER were described as examples of temperature control components, but the disclosed technology is not limited to this. As long as the component has a plurality of regions Z that can be individually controlled, it can also be a component other than the electrostatic chuck 118 and the edge ring ER (e.g., the electrode plate 134 of the upper electrode 130, the side wall of the processing container 112, etc.). Furthermore, in the ARX models of the above embodiments, the power supply voltage v(t) of the heater HT and the cooler temperature z(t) are included as explanatory variables, but the disclosed technology is not limited to this. When the power supply voltage v(t) and cooler temperature z(t) are not changed in the use of the substrate processing apparatus 10, the power supply voltage v(t) and cooler temperature z(t) may also be excluded as explanatory variables in the ARX model. Furthermore, as other embodiments, the frequency of the RF power, the magnitude of the RF power, the pressure inside the processing container 112, the type of gas supplied to the processing container 112, and the flow rate of the gas supplied to the processing container 112 may also be added as explanatory variables. Furthermore, the embodiments disclosed herein should be considered illustrative in all respects and not restrictive. In fact, the above embodiments can be embodied in various forms. Moreover, the above embodiments do not depart from the scope and spirit of the appended patent application and can be omitted, substituted, or modified in various forms. 1: Substrate processing system 10: Substrate processing device 20: Model data creation device 21: Communication I / F 22: User I / F 23: Control unit 24: Memory unit 100: Control device 101: Communication I / F 102: User I / F 103: Control unit 104: Memory unit 110: Device body 112: Processing container 112a: Grounding conductor 112e: Exhaust port 112g: Opening 114: Support unit 116: Stage 118: Electrostatic chuck 120: Base 122: DC power supply 124: Flow path 126: Piping 126a: Piping 126b: Piping 130: Upper electrode 132: Insulating shielding member 134: Electrode plate 134a: Gas 136: Body outlet; 136a: Support body; 136b: Gas diffusion chamber; 136c: Gas inlet; 138: Piping; 140: Gas source group; 142: Valve group; 144: Flow controller group; 146: Accumulated material shield; 148: Exhaust plate; 150: Exhaust device; 152: Exhaust pipe; 154: Gate valve; 160: Heater control circuit; 161: Control block; 161-1~161-n: Control block; 163: 164 Ammeter: 165 Voltmeter: Measurement Unit: 166 Power Supply: 230 Data Collection Unit: 231 Model Data Production Unit: 240 Temperature Control Data: 241 Weighting Factor: 1030 Data Collection Unit: 1031 Temperature Control Unit: 1032 Process Recipe Execution Unit: 1033 Model Data Update Unit: 1040 Correspondence Table: 1041 Model Data: 1042 Process Recipe: E1 Electrode: ER Edge Ring: HFS RF Power Supply: HT Heater: LFS RF Power Supply: MU Matching Unit: MU1 Matching Unit: MU2 Matching Unit: N Communication Network: S Processing Space: S100~S109 Steps: S200~S208 Steps: S300~S304 Steps: SW Switch: SW1 Switch: SW2 Switch: W Substrate: Z Region: Z1 Region: Z2 Region: Z3 Region: Z4 Region: Z6 Region: Z10 Region: Z13 Region: Figure 1 is a diagram showing an example of the configuration of a substrate processing system. Figure 2 is a schematic cross-sectional view showing an example of a substrate processing apparatus. Figure 3 is a top view showing an example of an electrostatic chuck and edge ring. Figure 4 is a diagram showing an example of a heater control circuit. Figure 5 is a diagram showing an example of a control device included in the substrate processing apparatus of the first embodiment. Figure 6A is a diagram showing an example of temperature control condition data. Figure 6B is a diagram showing an example of temperature control data. Figure 7 is a diagram showing an example of a model data production apparatus. Figure 8 is a flowchart showing an example of the processing of the model data production apparatus. Figure 9 is a diagram illustrating an example of a method for determining weighting factors. Figure 10 is a flowchart showing an example of the processing of the substrate processing apparatus. Figure 11 is a diagram showing an example of temperature changes in each region during temperature control in a comparative example. Figure 12 is a diagram showing the region of the evaluation object. Figure 13 is a diagram showing an example of temperature changes in each region during temperature control in this embodiment. Figure 14 is a diagram showing an example of a control device included in the substrate processing apparatus of the second embodiment. Figure 15 is a diagram illustrating an example of the update order of model data coefficients. Figure 16 is a diagram illustrating an example of the effect of adaptive control. Figure 17 is a flowchart illustrating an example of the application order of model data using applied control. Figure 18 is a diagram illustrating an example of the method for determining weighting factors when dealing with regions containing different materials. S100~S109: Steps

Claims

1. A model-based control method comprising the following steps: a) acquiring temperature control data, the temperature control data including temperature data of each region in a temperature control member disposed in a processing device and having a plurality of regions capable of individual temperature control; b) for each of the aforementioned regions, identifying the temperature of the other regions weighted by a weighting factor determined based on the magnitude of heat transfer between the other regions; c) for each of the aforementioned regions, identifying parameters of a multi-input single-output (MIMO) state-space model using the identified temperatures of the other regions and the temperature control data; d) generating a multi-input multiple-output (MIMO) state-space model by allocating the identified parameters of the MIMO state-space model to elements of a multi-input multiple-output (MIMO) state-space model; and e) using the MIMO state-space model to control the temperature of each of the aforementioned regions of the temperature control member.

2. The model-based control method of claim 1, comprising the following steps: f) obtaining temperature data of each of the aforementioned regions measured during the operation of the aforementioned processing device; and g) updating the parameters of each element of the aforementioned multi-input multi-output state-space model by adaptive control based on the error between the temperature predicted using the aforementioned multi-input multi-output state-space model and the temperature obtained in step f).

3. The model-based control method of claim 1 or 2, wherein the weighting factor of each of the above regions is determined based on the area or length of the boundary surface with the adjacent other regions, and the weighting factor relative to the non-adjacent other regions is 0.

4. The model-based control method of claim 1 or 2, wherein the weighting factor of each of the aforementioned regions is determined based on the magnitude of heat transfer caused by the difference between the material of the aforementioned region and the material of other regions adjacent to the aforementioned region.

5. The model-based control method as claimed in claim 1 or 2, wherein the processing apparatus is a substrate processing apparatus for processing a substrate, and the temperature control member is a stage for placing the substrate and controlling the temperature of the substrate.

6. The model-based control method of claim 1 or 2, wherein the aforementioned multi-input multi-output state-space model includes an item representing the temperature of the refrigerant controlled by the cooler unit cooling the plurality of the aforementioned regions, and an item representing the magnitude of the power supply voltage supplied to the heater heating the plurality of the aforementioned regions.

7. The model-based control method as described in request item 1 or 2, wherein the aforementioned multi-input single-output state-space model is an ARX (Auto-Regressive eXogenous) model.

8. The model-based control method as requested in item 1 or 2, wherein in step c) above, the parameters of the multi-input single-output state-space model are specified using Ordinary Least Squares regression (OLS), Lasso, Ridge, or Elastic Net.

9. The model-based control method of claim 1 or 2, wherein at least one of the plurality of regions differs from the other adjacent regions in at least one of the following aspects: the shape of the region, the shape of the boundary surface, or the material.

10. The model-based control method of claim 1 or 2, wherein the processing apparatus is a substrate processing apparatus for processing a substrate, and the temperature control data including the temperature of each of the aforementioned regions is obtained via a substrate placed on the temperature control member.

11. A model-based control system comprising a model data generation apparatus and a processing apparatus, the model data generation apparatus comprising: a first control unit configured to generate a state-space model; and an output unit configured to output the state-space model to the processing apparatus; the processing apparatus comprising: a temperature control member configured to have a plurality of regions capable of individually controlling temperature; a memory unit configured to acquire and store the state-space model generated by the model data generation apparatus; and a second control unit configured to use the state-space model stored in the memory unit to control the temperature of each of the regions of the temperature control member; the first control unit performing the following steps: a) acquiring temperature control data including data on the temperature of each of the regions of the temperature control member; b) for each of the regions, specifying the temperature of the other regions as a weighted average calculated by a weighting factor determined based on the magnitude of heat transfer between the other regions. c) For each of the above-mentioned regions, using the temperature of the other regions and the temperature control data, determine the parameters of the multi-input single-output state-space model; and d) By assigning the parameters of the determined multi-input single-output state-space model to the elements of the multi-input multiple-output state-space model, the multi-input multiple-output state-space model is created.

12. The model-based control system of claim 11, wherein the second control unit performs the following steps: e) using the multi-input multi-output state-space model stored in the memory unit to control the temperature of each region of the temperature control member; f) obtaining temperature data of each region measured during the operation of the processing device; and g) updating the parameters of each element of the multi-input multi-output state-space model by adaptive control based on the error between the temperature predicted using the multi-input multi-output state-space model and the temperature obtained in step f).

13. A program that causes a computer to perform the following steps: a) acquiring temperature control data, the temperature control data including temperature data of each of the regions in a temperature control member disposed in a processing device and having a plurality of regions capable of individually controlling temperature; b) for each of the regions, specifying the temperature of the other regions by weighted averaging based on a weighting factor determined according to the magnitude of heat transfer between the other regions; c) for each of the regions, specifying parameters of a multi-input single-output state-space model using the specified temperature of the other regions and the temperature control data; and d) generating the multi-input multiple-output state-space model by distributing the specified parameters of the multi-input single-output state-space model to the elements of a multi-input multiple-output state-space model.

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