Substrate processing method, semiconductor device manufacturing method, substrate processing apparatus, and recording medium

Abstract

Provided is a technique for controlling the supply of power to a heater in such a manner that a predicted temperature series calculated from a prediction model held in advance approaches a target temperature series for the future, and a technique for updating the aforementioned target temperature series for the future in accordance with the current temperature, the final target temperature, and a temperature convergence ramp rate.

Description

Technical Field

[0001] This disclosure relates to substrate processing methods, semiconductor device manufacturing methods, substrate processing apparatus, and recording media. Background Technology

[0002] In semiconductor manufacturing apparatus, for example, a substrate is housed in a furnace to form a thin film on a processing substrate, and the furnace is heated. Furthermore, in order to maintain the furnace at an appropriate temperature or to make the furnace follow a specified temperature change, a control device performs temperature control based on a preset temperature.

[0003] For commonly used temperature control, feedback control based on proportional-integral-derivative (PID) calculations is used to control the electrical power of the heater in the furnace in a manner close to the desired temperature. In this PID-based feedback control, appropriate proportional, integral, and derivative parameters (hereinafter referred to as PID parameters) need to be predetermined. For these PID parameters, it is preferable to determine the optimal values ​​based on the temperature characteristics of the heater.

[0004] For example, Patent Document 1 discloses a semiconductor manufacturing apparatus having a switch that switches and outputs an operational quantity output by a pattern generation unit and an operational quantity output by an adjustment unit that receives a target value and a control detection value via an adder. Patent Document 2 discloses a semiconductor manufacturing apparatus that automatically acquires temperature characteristics in advance and uses those characteristics for temperature control, thereby preventing deviations in control performance caused by the adjustment operator.

[0005] However, in such temperature control, when the substrate holder containing the substrate is placed into the furnace, the furnace temperature temporarily drops and then recovers to the original furnace temperature, resulting in an overshoot, and the recovery time until convergence becomes longer.

[0006] Existing technical documents

[0007] Patent documents

[0008] Patent Document 1: Japanese Patent Application Publication No. 2000-183072

[0009] Patent Document 2: Japanese Patent Application Publication No. 2019-145730 Summary of the Invention

[0010] The problem that the invention aims to solve

[0011] This disclosure provides a technique for suppressing overshoot and rapidly converging toward the target temperature when inserting a substrate holder into a furnace.

[0012] Methods for solving problems

[0013] According to one aspect of this disclosure, a technique is provided for controlling the power supply to a current heater in such a way that the predicted temperature series calculated according to a pre-held prediction model approaches the future target temperature series, wherein the aforementioned future target temperature series is updated based on the current temperature, the final target temperature, and the temperature convergence using a ramp rate.

[0014] Invention Effects

[0015] According to this disclosure, over-adjustment can be suppressed, allowing the furnace temperature to converge rapidly to the target temperature. Attached Figure Description

[0016] [ Figure 1 This is a longitudinal sectional view of a processing furnace of a substrate processing apparatus according to one embodiment of the present disclosure.

[0017] [ Figure 2 This is a schematic diagram illustrating an example of a configuration for temperature regulation of a heater using a temperature control unit, according to one embodiment of this disclosure.

[0018] [ Figure 3 This is a block diagram illustrating the control configuration of a temperature control unit according to one embodiment of the present disclosure.

[0019] [ Figure 4 ] Figure 4 (A) Figure 4 (D) is to show the storage in Figure 3 The diagram shows an example of data in the storage area of ​​the predictive model.

[0020] [ Figure 5 To show the storage in Figure 3 A diagram showing another example of data in the storage area of ​​the predictive model.

[0021] [ Figure 6 [This is a control block diagram of the internal temperature control unit according to one embodiment of this disclosure.]

[0022] [ Figure 7 This is a flowchart illustrating the first effective constraint method used in this disclosure.

[0023] [ Figure 8 [A flowchart illustrating the second effective constraint method used in this disclosure.]

[0024] [ Figure 9 This is a flowchart illustrating an example of an automatic acquisition step of the thermal characteristics of a temperature control unit according to one embodiment of this disclosure.

[0025] [ Figure 10 ]for Figure 9 The diagram shows the internal control block of the temperature control unit in the example of the automatic acquisition step.

[0026] [ Figure 11 ] Figure 11 (A) is a flowchart illustrating an example of a substrate processing procedure. Figure 11 (B) is shown Figure 11 A graph showing the temperature changes inside the furnace during each processing step of (A).

[0027] [ Figure 12 This is for use with the temperature control unit according to the first embodiment of this disclosure. Figure 11 The diagram illustrates the process in step S102 of (A).

[0028] [ Figure 13 This is for use with the temperature control unit according to the second embodiment of this disclosure. Figure 11 The diagram illustrates the process in step S102 of (A).

[0029] [ Figure 14 This is for use with the temperature control unit according to the third embodiment of this disclosure. Figure 11 The diagram illustrates the process in step S102 of (A).

[0030] [ Figure 15 This is a graph showing the temperature trajectory inside the furnace based on the temperature control involved in the comparative example.

[0031] [ Figure 16 ] Figure 16 (A) is a diagram showing the temperature trajectory inside the furnace based on the temperature control involved in this embodiment. Figure 16 (B) is a graph showing the temperature trajectory inside the furnace based on the temperature control involved in this embodiment, and the number of substrates inside the furnace is set to... Figure 16 The diagram is made by dividing (A) by half. Detailed Implementation

[0032] <One embodiment of this disclosure>

[0033] The following describes one embodiment of this disclosure.

[0034] Figure 1This is a schematic configuration diagram of the processing furnace 202 of the substrate processing apparatus used in the manufacture of a semiconductor device according to one embodiment of this disclosure, shown in the form of a longitudinal sectional view. It should be noted that the drawings used in the following description are schematic, and the dimensional relationships and ratios of the elements shown in the drawings may not be consistent with reality. Furthermore, the dimensional relationships and ratios of the elements may not be consistent between the various drawings.

[0035] like Figure 1 As shown, the processing furnace 202 has a heater 206 as a heating mechanism. The heater 206 is cylindrical in shape and is vertically mounted by being supported by a heater base 251, which serves as a retaining plate.

[0036] Inside the heater 206, a heat spreader (outer tube) 205 is arranged concentrically with the heater 206. This heat spreader is made of a heat-resistant material such as silicon carbide (SiC) and has a cylindrical shape that is closed at the top and open at the bottom. Inside the heat spreader 205, a reaction tube (inner tube) 204 is arranged concentrically with the heat spreader 205. This reaction tube (inner tube) 204 is made of a heat-resistant material such as quartz (SiO2) and has a cylindrical shape that is closed at the top and open at the bottom. A processing chamber 201 is formed in the hollow portion of the reaction tube 204, configured to accommodate a multi-layered wafer 200 (serving as a substrate) arranged horizontally in the vertical direction via a crystal boat 217 (described later).

[0037] A gas inlet 230 is provided at the lower end of the reaction tube 204. A thin tube 234, serving as a gas inlet tube, is arranged along the outer wall of the reaction tube 204 from the gas inlet 230 to the top 233 of the reaction tube 204. Gas introduced from the gas inlet 230 flows within the thin tube 234 and reaches the top 233, and is then introduced into the processing chamber 201 through a plurality of gas inlets 233a provided at the top 233. In addition, at a different position at the lower end of the reaction tube 204 than the gas inlet 230, a gas exhaust section 231 is provided to exhaust the atmosphere inside the reaction tube 204 through an exhaust port 231a.

[0038] A gas supply pipe 232 is connected to the gas inlet section 230. On the upstream side of the gas supply pipe 232, opposite to the connection side of the gas inlet section 230, a processing gas supply source (not shown), a carrier gas supply source, and a non-reactive gas supply source are connected via an MFC (mass flow controller) 241, which functions as a gas flow controller. It should be noted that when water vapor needs to be supplied to the processing chamber 201, a water vapor generator (not shown) is provided on the downstream side of the gas supply pipe 232, above the MFC 241. A gas flow control unit 235 is electrically connected to the MFC 241, configured to control the flow rate of the supplied gas at a desired time in such a way that the flow rate is the desired amount.

[0039] A gas exhaust pipe 229 is connected to the gas exhaust section 231. On the downstream side of the gas exhaust pipe 229, opposite to the connection side of the gas exhaust section 231, an exhaust device 246 is connected via a pressure sensor 245 (which acts as a pressure detector) and a pressure regulating device 242, configured to exhaust gas in a manner that ensures the pressure in the processing chamber 201 reaches a predetermined pressure. A pressure control unit 236 is electrically connected to the pressure regulating device 242 and the pressure sensor 245. The pressure control unit 236 is configured to control the pressure in the processing chamber 201 at a desired time based on the pressure detected by the pressure sensor 245 and using the pressure regulating device 242 to achieve the desired pressure.

[0040] At the lower end of the reaction tube 204, there is a base 257 serving as a retainer capable of airtightly sealing the lower opening of the reaction tube 204, and a sealing cover 219 serving as a furnace opening cover. The sealing cover 219 is made of a metal such as stainless steel and is formed in a disc shape. The base 257 is made of a quartz, for example, and is formed in a disc shape, and is mounted on the sealing cover 219. An O-ring 220 serving as a sealing member is provided on the upper surface of the base 257, abutting against the lower end of the reaction tube 204. On the side of the sealing cover 219 opposite to the processing chamber 201, there is a rotation mechanism 254 for rotating the crystal boat. The rotation shaft 255 of the rotation mechanism 254 passes through the sealing cover 219 and the base 257, and is connected to the heat insulation cylinder 218 and the crystal boat 217, so as to rotate the wafer 200 by rotating the heat insulation cylinder 218 and the crystal boat 217. The sealing cover 219 is configured to move vertically by means of a crystal boat lift 115, which is vertically mounted outside the reaction tube 204 and serves as a lifting mechanism, thereby enabling the crystal boat 217 to be moved in and out of the processing chamber 201. The drive control unit 237 is electrically connected to the rotating mechanism 254 and the crystal boat lift 115, and is configured to control the operation at a desired time in a desired manner.

[0041] The crystal boat 217, serving as a substrate holder, is made of a heat-resistant material such as quartz or silicon carbide, and is configured to hold multiple wafers 200 in a horizontal orientation and with their centers aligned. Below the crystal boat 217, a cylindrical heat insulation cylinder 218, made of a heat-resistant material such as quartz or silicon carbide, is provided to support the crystal boat 217. The heat insulation cylinder 218 is configured to prevent heat from the heater 206 from being easily transferred to the lower end of the reaction tube 204.

[0042] In the processing furnace 202, two types of sensors are provided as temperature detectors. Specifically, a first temperature sensor 263 is installed between the reaction tube 204 and the heat spreader 205. Additionally, a second temperature sensor 264 is installed between the heat spreader 205 and the heater 206. Both the first temperature sensor 263 and the second temperature sensor 264 use multiple thermocouples to detect the temperature. Details regarding the first temperature sensor 263 and the second temperature sensor 264 will be described later. A temperature control unit 238 is electrically connected to the heater 206, the first temperature sensor 263, and the second temperature sensor 264.

[0043] The main control unit 240 comprises a gas flow control unit 235, a pressure control unit 236, a drive control unit 237, a temperature control unit 238, and an operation unit 239. The operation unit 239 includes input / output units (not shown) and a display unit, and is configured to exchange data with the gas flow control unit 235, pressure control unit 236, drive control unit 237, and temperature control unit 238. Furthermore, a host controller 36 is connected to the main control unit 240. Similar to the operation unit 239, the host controller 36 includes input / output units, and can be configured to control the main control unit 240.

[0044] Figure 2 This is a schematic diagram illustrating an example of a configuration in which a first temperature sensor 263 and a second temperature sensor 264 are used, and the temperature of the heater 206 is adjusted by a temperature control unit 238.

[0045] Figure 2 In the example shown, the heater 206 is divided into 5 parts along the vertical direction, and each region is designated as region a, region b, region c, region d, and region e from top to bottom.

[0046] The first temperature sensor 263 detects the temperature between the reaction tube 204 and the heat spreader 205. The first temperature sensor 263 is equipped with thermocouples 263a, 263b, 263c, 263d, and 263e, which are cascaded thermocouples, corresponding to each region.

[0047] The second temperature sensor 264 detects the temperature between the heat spreader 205 and the heater 206. The second temperature sensor 264 is equipped with thermocouples 264a, 264b, 264c, 264d, and 264e, which are thermocouples for the heater, respectively, corresponding to each region.

[0048] That is, it is configured to adjust the energization of each area of ​​the heater 206 by using the temperature control unit 238 based on the temperature information detected by thermocouples 263a-263e and thermocouples 264a-264e, so that the temperature of the processing chamber 201 is controlled at the desired time in a manner that is set by the upper controller 36.

[0049] In the following text, the temperature detected by the second temperature sensor 264 (thermocouples 264a to 264e) will be used as the heater temperature, and the temperature detected by the first temperature sensor 263 (thermocouples 263a to 263e) will be used as the furnace temperature.

[0050] Figure 3 A block diagram illustrating the control configuration of the temperature control unit 238 is provided.

[0051] like Figure 3 As shown, the temperature control unit 238 includes a CPU 712, a communication interface (IF) 716, a power supply unit 718, a display / input device 720, and a temperature input circuit 722. These components are interconnected via a control bus 714. Furthermore, the memory or storage device connected to the control bus 714, which serves as a storage unit, includes a program storage area 726, a prediction model storage area 854, a temperature history storage area 850, a power supply value history storage area 852, and a parameter storage area 856.

[0052] In the temperature history storage area 850, the historical temperature data (heater temperature information) of the heater, detected by the second temperature sensor 264 via the temperature input circuit 722, is stored for a certain period of time. In addition, the historical temperature data (furnace temperature information) of the processing chamber 201, detected by the first temperature sensor 263 via the temperature input circuit 722, is also stored for a certain period of time.

[0053] In the power supply value history storage area 852, the history (power supply value information) of the power supply value (0-100%) of the heater 206 is only stored for a certain period of time.

[0054] In the prediction model storage area 854, prediction models for predicting the predicted temperature of at least one of the heater temperature and furnace temperature are stored for each temperature zone. Specifically, the prediction model stores the coefficients involved, the coefficient error correlation matrix (described later), the reference temperature, and the stable power value. The coefficients involved, the coefficient error correlation matrix, the reference temperature, and the stable power value are stored separately for the heater temperature and furnace temperature of each zone. Furthermore, for prediction models related to the heater temperature and furnace temperature of all zones, all of the above are stored as one group, and multiple groups are stored corresponding to each temperature zone. Thus, it is configured in a way that can correspond to multiple temperature zones.

[0055] Here, the reference temperature refers to the temperature when the heater temperature and furnace temperature are in a stable state. Furthermore, the so-called stable power value refers to the reference value of the prediction model, and is the power supply value for each region when the heater temperature and furnace temperature are at the reference temperature and in a stable state.

[0056] For example, in the prediction model storage area 854, the following are stored in tabular form: Figure 4 or Figure 5 The data shown is related to the prediction model.

[0057] Figure 4 (A) is the baseline value related to the prediction model of the heater temperature in region a, representing the power supply of each region when the heater temperature in region a is at the baseline temperature and in a steady state, with the baseline temperature set at 101°C. Figure 4 (B) represents the baseline value related to the prediction model of the heater temperature in region b, indicating the power supply of each region when the heater temperature in region b is at the baseline temperature and in a steady state, with the baseline temperature set at 111°C. The same table is then created and stored for regions c through e.

[0058] Figure 4 (C) is the baseline value related to the prediction model of the furnace temperature in region a, representing the power supply of each region when the furnace temperature in region a is the baseline temperature and in a steady state, with the baseline temperature set at 202°C. Figure 4 (D) represents the baseline value related to the prediction model of the furnace temperature in region b, indicating the power supply of each region when the furnace temperature in region b is at the baseline temperature and in a steady state, with the baseline temperature set at 212°C. The same table is then created and stored for regions c through e.

[0059] Figure 5The following scenario illustrates an example where, for instance, the power supply to area a is set to 10%, to area b to 20%, to area c to 30%, to area d to 40%, and to area e to 50%, and this state is maintained. After sufficient time, a steady state is reached where the heater temperature in area a is 100°C and the furnace temperature is 200°C, the heater temperature in area b is 110°C and the furnace temperature is 210°C, the heater temperature in area c is 120°C and the furnace temperature is 220°C, the heater temperature in area d is 130°C and the furnace temperature is 230°C, and the heater temperature in area e is 140°C and the furnace temperature is 240°C. In this case, although it is necessary to match the power supply values ​​under steady-state conditions, it is related to... Figure 4 Compared to the situation shown, the storage area can be reduced.

[0060] The parameter storage area 856 stores various parameters used to implement the prediction model.

[0061] The program storage area 726 stores a temperature control program that controls the process by selecting a prediction model within a specified temperature band, inputting temperature data, and predicting the optimal temperature. Additionally, the program storage area 726 stores a program that causes the substrate processing apparatus to perform the following steps: controlling the current heater power supply in a manner that makes the predicted temperature series calculated based on a pre-held furnace temperature prediction model approach the future target temperature series.

[0062] The CPU 712 executes prescribed processing based on the temperature control program stored in the program storage area 726 in the memory or storage device. The CPU 712 can communicate with the host controller 36 via the communication IF 716 to obtain the target temperature. In addition, the CPU 712 can detect the furnace temperature and the heater temperature, and output control signals to the power supply unit 718 via the temperature input circuit 722 to control and supply power to each zone a to zone e of the heater 206 respectively.

[0063] That is, the temperature control unit 238 is configured to obtain temperature history, power supply value history, and various parameters from the temperature history storage area 850, the power supply value history storage area 852, and the parameter storage area 856, respectively, and execute a temperature control program using the prediction model stored in the prediction model storage area 854, thereby controlling the heater 206. In this embodiment, an example of the procedure in which the temperature control unit 238 executes the following steps to make the substrate processing apparatus perform: controlling the power supply to the heater in such a way that the predicted temperature series calculated based on the pre-held furnace temperature prediction model is close to the future target temperature series. In addition, in this embodiment, the configuration also includes a step of generating a characteristic equation using the prediction model and a step of calculating the solution of the characteristic equation.

[0064] The display / input device 720 can display and input various parameters stored in the parameter storage area 856.

[0065] [Prediction Model]

[0066] Next, the prediction model stored in the prediction model storage area 854 described above will be explained. Here, the prediction model refers to the mathematical formula used to calculate the predicted temperature, which is Equation 1 below.

[0067] [Mathematical Expression 1]

[0068] Δy(t)=a1·y(t-1)+a2·y(t-2)+ma1·p a (t-1)+ma2·p a (t-2)+...+ma n ·p a (tn)+mb1·p b (t-1)+mb2·p b (t-2)+...+mb n ·p b (tn)+mc1·p c (t-1)+mc2·p c (t-2)+...+mc n ·p c (tn)+md1·p d (t-1)+md2·p d (t-2)+...+md n ·p d (tn)+me1·p e (t-1)+me2·p e (t-2)+...+me n ·p e (tn)+bi...(Equation 1)

[0069] Here, Δy(t) is the deviation of the predicted temperature from the reference temperature at time t. Additionally, y(t-1) and y(t-2) are the deviations of the temperatures one and two times prior from the reference temperature. Furthermore, p... a (t-1), p a (t-2), ..., p a (tn) represents the deviation of the power supply value from the stable power value in region a 1st, 2nd, ..., nth time ago, p b (t-1), p b (t-2), ..., p b (tn) represents the deviation of the power supply value of region b from the stable power value 1, 2, ..., n years ago, p c (t-1), p c (t-2), ..., p c (tn) represents the deviation of the power supply value of region c from the stable power value 1, 2, ..., n times ago, p d (t-1), p d (t-2), ..., p d (tn) represents the deviation of the power supply value from the stable power value in region d 1, 2, ..., n years ago, p e (t-1), p e (t-2), ..., p e (tn) represents the deviation of the power supply value of region e from the stable power value 1, 2, ..., n years ago.

[0070] a1, a2, ma1, ..., ma n mb1, ..., mb n ,mc1,...,mc n md1, ..., md n me1, ..., me n These are their respective coefficients. bi is the constant term. n is a value preset in parameter storage area 856.

[0071] Here, Δy(t) represents the deviation between the predicted temperature and the reference temperature at time t, so the final predicted temperature is (Δy(t) + reference temperature). However, Δy(t) itself is sometimes simplified and denoted as the predicted temperature below.

[0072] The prediction model can store heater temperature and furnace temperature separately for each region and use them for control calculations. Specifically, for example, it can store prediction models related to the predicted furnace temperature in region a, prediction models related to the predicted heater temperature in region e, and so on. It should be noted that the temperatures shown in Equation 1 above include both heater temperature and furnace temperature.

[0073] In the automatic acquisition step of thermal characteristics described later, the reference temperature and stable power value are obtained in the preliminary stage of creating the prediction model. The constant term bi is an adjustment term for deviations between the pre-obtained reference temperature and stable power value and the actual value. If the pre-obtained reference temperature and stable power value do not change over time, the constant term of the prediction model shown in Equation 1 obtained after the automatic acquisition step of thermal characteristics is expected to be bi = 0. However, due to changes in the surrounding environment, power fluctuations, thermocouple noise, etc., the reference temperature and stable power value change constantly, and are therefore included in the prediction model (Equation 1).

[0074] Furthermore, the reference temperature and stable power values ​​vary depending on the temperature range of the object, and are assumed to be non-linear. If the reference temperature and stable power values ​​are incorrect, the accuracy of temperature prediction will decrease, affecting control performance. Therefore, it is preferable that the reference temperature and stable power values ​​are obtained near the aforementioned specified processing temperature in the oxidation-diffusion treatment described above.

[0075] According to Equation 1, under the conditions of a reference temperature, a stable power supply, and this state continuing, y(t-1) and y(t-2) are zero, and p a (t-1), ..., p a (tn), ..., p e (t-1), ...p e (tn) are also all zero, resulting in Δy(t) = bi, therefore the predicted temperature = bi + reference temperature. If the reference temperature and the stable power value remain unchanged, we get bi = 0, then the predicted temperature = reference temperature. This means that under the steady-state condition at the reference temperature, the prediction model in Equation 1 is appropriate.

[0076] Furthermore, according to Equation 1 above, it is shown that, for example, if the prediction model is related to the furnace temperature in region a, then depending on the coefficients, not only does the power supply in region a affect the furnace temperature in region a, but the power supply in regions b, c, etc., also affects the furnace temperature in region a. Thus, depending on the coefficients, the mutual thermal interference between regions can be represented.

[0077] Furthermore, the prediction model of Equation 1 above predicts the temperature around a set of reference temperatures. Assuming that the temperature rise and fall characteristics differ depending on the temperature band being considered, prediction models for multiple temperature bands can be stored in the prediction model storage area 854, and any one of them can be selected.

[0078] In addition, for the purpose of simplifying calculations, the following Equation 2 is sometimes used instead of the prediction model for heater temperature.

[0079] [Mathematical Expression 2]

[0080] Δy h (t)=a1·y h (t-1)+a2·y h (t-2)+m1·p(t-1)+m2·p(t-2)+...+m n ·p(tn)+bi...(Equation 2)

[0081] Here, Δy h (t) represents the deviation between the predicted heater temperature and the reference temperature at time t. Additionally, y h (t-1), y h (t-2) represents the deviation of the heater temperature from the reference temperature before the first and second cycles, p(t-1), p(t-2), ..., p(tn) represent the deviation of the power supply value from the stable power value in the corresponding region before the first, second, ..., n cycles, and a1, a2, m1, m2, ..., m n These are their respective coefficients. bi is the constant term. n is a value preset in parameter storage area 856.

[0082] That is, in Equation 2 above, only the power supply value from the corresponding region affects the predicted heater temperature. Therefore, thermal interference from outside the corresponding region is not considered. For example, when calculating the predicted heater temperature for region a, only the power supply value for region a is used. The reason for this is that, as... Figure 2 As shown, the thermocouple 264a of the second temperature sensor 264 is located near the heater 206, so it is assumed that it is completely unaffected by the heat of the heater 206 in the other separated areas or that the heat is so small as to be negligible.

[0083] Furthermore, in Equation 2, compared to Equation 1, the computational cost of product summation is reduced, thus making the process of calculating the predicted temperature faster. In addition, the number of coefficients in the prediction model that should be obtained from the automatic acquisition step of thermal characteristics described later is reduced, thus offering the advantage of faster processing.

[0084] Figure 6 This is a diagram showing the internal control block diagram of the temperature control unit 238.

[0085] like Figure 6 As shown, the host controller 36 and the temperature control unit 238 are connected to the heater 206. The target temperature from the host controller 36 is input at input terminal S. The furnace temperature from the first temperature sensor 263 is input at input terminal F. The heater temperature from the second temperature sensor 264 is input at input terminal H.

[0086] The target temperature and the input terminal S exist in a number corresponding to the number of thermocouples 263a to 263e of the first temperature sensor 263, but since they are of the same configuration, therefore... Figure 6 Only one is shown in the diagram. Similarly, the number of input terminals F corresponds to the number of thermocouples 263a to 263e of the first temperature sensor 263, but since they are of the same configuration, therefore... Figure 6 Only one is shown in the diagram. Similarly, the number of input terminals H corresponds to the number of thermocouples 264a to 264e of the second temperature sensor 264, but since they are of the same configuration, therefore... Figure 6 Only one is shown in the image.

[0087] The temperature control unit 238 is internally composed of a temperature history storage unit 800, a power supply value history storage unit 802, an individual characteristic production unit 804, a target temperature calculation unit 870, a comprehensive characteristic production unit 808, a constrained optimization calculation unit 810, a limiter 812, and a power supply unit 718.

[0088] The temperature history storage unit 800 receives the furnace temperature from the first temperature sensor 263 via input terminal F and stores it in the temperature history storage area 850 for a certain period of time. Starting from the initially acquired furnace temperature, the temperature history storage unit 800 sequentially writes data into the temperature history storage area 850 at predetermined intervals. When the temperature history storage area 850 is full, the oldest data is discarded, and new data is written to that location. In this way, data on the furnace temperature up to a certain time ago is always stored.

[0089] To ensure a consistent understanding of time, the furnace temperature written in the processing of time t shown in the control algorithm is treated as y(t-1) (the temperature before time 1) in Equation 1. The obtained furnace temperature is calculated based on the average electromotive force of thermocouples 263a to 263e up to the writing time.

[0090] The power supply value history storage unit 802 receives the power supply value output from the output terminal P and stores this data in the power supply value history storage area 852 for a certain period of time. Starting from the first acquired power supply value, the power supply value history storage unit 802 sequentially writes data into the power supply value history storage area 852 at predetermined intervals. When the power supply value history storage area 852 is full, the oldest data is discarded, and new data is written to that location. In this way, data on past power supply values ​​up to a certain time ago is always stored.

[0091] To ensure a consistent understanding of time, the power supply value written in the processing of time t in the control algorithm is used as p in Equation 1. a (t-1), p b (t-1), p c (t-1), p d (t-1), p e The process is performed on (t-1) (the power supply value before step 1). It represents the value of the power calculated from the previous process and continuously supplied up to the current moment.

[0092] The individual characteristic production unit 804 obtains the prediction model of the furnace temperature in that region from the prediction model storage area 854, obtains the current and past data of the specified furnace temperature from the temperature history storage area 850, and obtains the current and past data of the specified power supply value from the power supply value history storage area 852, and calculates the individual input response characteristic matrix S as described in Equations 3 and 4 below. sr and individual zero-response characteristic vectors S zr Regarding the individual input response characteristic matrix S sr and individual zero-response characteristic vectors S zr In this regard, only the number of furnace temperatures that are the controlled objects is calculated (= number of zone divisions).

[0093] Equation 1 above can be represented by the state-space model shown in Equation 3 below.

[0094] [Mathematical Expression 3]

[0095]

[0096] Here, matrices A, B, and C are as follows. It should be noted that, for simplicity, the deviations between the power supply values ​​and the stable power values ​​from regions a to c in the first four instances (n=4) are used. It should also be noted that although the examples below use regions a to c in the first four instances for simplicity, they are not limited to this.

[0097] [Mathematical Expression 4]

[0098]

[0099]

[0100] C = [1 0 0 0 0 0 0 0 0 0 0]

[0101] Furthermore, the vectors x(t), u(t), and output y(t) are as follows. To simplify the description, we continue to use the deviations between the power supply values ​​and the stable power values ​​from regions a to c for the first four times (n=4).

[0102] [Mathematical Expression 5]

[0103]

[0104]

[0105] y(t)=Δy(t)

[0106] In Equation 3, if the power supply value u(t) is input at time t and then u(t) is input directly, the predicted temperature after t+1 becomes Equation 4.

[0107] [Mathematical Expression 6]

[0108]

[0109] Δy(t)=s zr +s sr ·u(t)...(Equation 4)

[0110] in,

[0111]

[0112]

[0113] Here, in Equation 4, S zr S is an individual zero-response characteristic vector. sr Let be the individual input response characteristic matrix, and Δy(t) be the predicted temperature vector. The predicted temperature vector refers to the case where the predicted temperature column is represented in vector form.

[0114] The numbers in each row are the calculated numbers for the predicted temperature, and only the number allowed by the control cycle and the processing performance of the CPU712 is calculated.

[0115] Individual zero response characteristic vector S zr This represents the change in the predicted temperature vector Δy(t) due to the influence of past furnace temperatures and past power supply values. Additionally, the individual input response characteristic matrix S... srThis represents the change in the predicted temperature vector Δy(t) due to the influence of the calculated power supply value.

[0116] Below, when the individual input response characteristic matrix S is... sr Individual zero-response characteristic vector S zr When the predicted temperature vector Δy(t) is distinguished according to the corresponding region, the individual input response characteristic matrix corresponding to region a is expressed as S. sr-a The individual zero-response characteristic vector corresponding to region b is represented by S. zr-b The predicted temperature vector corresponding to region e is represented by Δy. e (t), etc.

[0117] Regarding the target temperature column calculation unit 870, the target temperature is input from the host controller 36 via input terminal S, and the furnace temperature is input from input terminal F. The unit calculates a target temperature column vector S, which represents the target value of future temperature changes in vector form. tg The current target temperature, the final target temperature, and the ramp rate are provided from the input terminal S at a certain control cycle. The ramp rate refers to the proportion of temperature change from the current target temperature to the final target temperature, representing the amount of temperature change per unit time. For example, if set to 1℃ / minute, it means a change of 1℃ per minute. Inputting the target temperature, the final target temperature, and the ramp rate, the target temperature column vector S is calculated. tg .

[0118] Furthermore, the host controller 36 provides the target temperature column calculation unit 870 with a temperature convergence ramp rate at any time and within a preset period. The temperature convergence ramp rate refers to the proportion of change from the current temperature (i.e., the current furnace temperature) to the final target temperature, representing the amount of temperature change per unit time. For example, if set to 1°C / minute, it means a change of 1°C per minute. During the period when the temperature convergence ramp rate is provided, the target temperature column calculation unit 870 replaces the ramp rate using the current target temperature with the proportion of change using the temperature convergence ramp rate using the current temperature (i.e., the current furnace temperature), thereby calculating the target temperature column vector S up to the final target temperature. tg At this point, the target temperature column vector S is calculated by inputting the current furnace temperature, the final target temperature, and the temperature convergence ramp rate. tg That is, during a pre-defined period, such as a period prone to overshoot, the target temperature column vector S, which serves as the future target temperature column, is updated according to the current temperature (i.e., the current furnace temperature), the final target temperature, and the temperature convergence ramp rate. tg Therefore, over-adjustment can be suppressed, and the furnace temperature can be quickly converged to the target temperature.

[0119] Regarding the target temperature column vector S tg In this regard, only the number of furnace temperatures (i.e., the number of zone divisions) that are the controlled objects are calculated. For the following explanation, the target temperature column vector S... tg As stated in Equation 5 below.

[0120] [Mathematical Expression 7]

[0121]

[0122] The time and row number in Equation 5 correspond to those in Equation 4. The target temperature column vector S will be described below. tg When distinguishing by corresponding regions, the case corresponding to region a is described as S. tg-a The case corresponding to region e is represented as S. tg-e ,etc.

[0123] From the temperature history storage unit 800 to the target temperature calculation unit 870, the heater 206 is divided, and therefore exists in a number corresponding to the number of divisions along with the input terminals S and F, but for simplicity... Figure 6 Only one is shown in the diagram.

[0124] For the comprehensive characteristic production unit 808, the input is the individual input response characteristic matrix S obtained by the individual characteristic production unit 804, which has a number of region divisions. sr and individual zero-response characteristic vectors S zr The input is the target temperature column vector S obtained by the target temperature column calculation unit 870 with the number of region divisions. tg Construct a comprehensive characteristic equation.

[0125] First, the individual input response characteristic matrix S sr Deformation. Individual input response characteristic matrix S sr This represents the predicted temperature change when u(t) is input at time t and then u(t) is directly input again. If u(t) is not kept constant but different values ​​u(t) ~ u(t+Np-1) are input at all control times, then the second term on the right side of Equation 4 becomes the following. Here, Np is the row number of Equation 4.

[0126] [Mathematical Expression 8]

[0127]

[0128] In well-known model predictive control, it is assumed that different values ​​u(t) ~ u(t+Np-1) are input at all computational processing times, and the result is obtained by calculation. However, due to the insufficient processing performance of the CPU712, the input pattern is limited to two stages in this disclosure, thereby making the second term on the right side of Equation 4 as follows.

[0129] [Mathematical Expression 9]

[0130]

[0131]

[0132] Here, Ncd is the number of input rows held in the first stage. The input u(t) of the first stage is held up to time t + Ncd - 1. For the input of the second stage, u(t + Ncd) is held up thereafter. The individual input response characteristic matrix S is thus represented. sr By transformation, Equation 4 yields Equation 6 as follows.

[0133] [Mathematical Expression 10]

[0134] Δy(t)=S zr +S dsr ·u cd (t)...(Equation 6)

[0135] in,

[0136]

[0137]

[0138] In Equation 6, S is re-evaluated. dsr Let S be the individual input response characteristic matrix. When distinguishing by corresponding regions, the individual input response matrix corresponding to region a is represented as S. dsr-a wait.

[0139] Next, Equations 6 and 5 above will be arranged as the entire area controlled by the above.

[0140] [Mathematical Expression 11]

[0141]

[0142]

[0143] As described above, the integrated characteristic production unit 808 calculates and outputs the integrated input-response characteristic matrix U shown in Equations 7 and 8. dsr Comprehensive zero-response characteristic vector U zr Comprehensive target temperature vector U tg .

[0144] Next, the constrained optimization calculation unit 810 inputs the comprehensive input response characteristic matrix U obtained by the comprehensive characteristic production unit 808. dsr Comprehensive zero-response characteristic vector U zr Comprehensive target temperature vector Utg Furthermore, the upper and lower limit values ​​of each region used in the limiter 812 described later are input, and the optimal power supply value is calculated using an effective constraint method that finds the minimum solution under the specified constraints. The effective constraint method and the operation of the constrained optimization calculation unit 810 applying it will be described later.

[0145] Then, limiter 812 restricts the calculation result to the range that heater 206 can output, as the power supply value to heater 206. Here, the output of limiter 812 is set as a ratio to the maximum output of heater 206, for example, limited to 0-100%. The output range of limiter 812 may vary depending on the heating temperature of heater 206. Therefore, the heater temperature can be obtained from input H, and a limit value can be derived from a temperature limit table (not shown) corresponding to the heater temperature, using this value for limitation. Then, other processing units can use the upper and lower limits of the output range to display the values.

[0146] Then, the power supply unit 718 controls the power supplied to the heater 206 via the output terminal P in a manner that corresponds to the power supply value of 0 to 100%.

[0147] It should be noted that, because the heater is divided, the limiter 812 and the power supply unit 718, together with the output terminal P, exist in a number corresponding to the number of divisions, but... Figure 6 For simplicity, only one is shown in the diagram.

[0148] [First Effective Restraint Method]

[0149] The first effective constraint method used in this disclosure is explained.

[0150] The effective constraint method is to find the solution vector x that maximizes the evaluation function f(x) provided by Equation 9 based on the constraint conditions of Equation 10 below.

[0151] [Mathematical Expression 12]

[0152]

[0153] b≥A·x...(Equation 10)

[0154] In Equations 9 and 10, c, Q, b, and A are provided constant matrices or vectors. Additionally, the symbol T denotes transpose. At this point, the effective constraint method can be implemented... Figure 7 The process shown is used to find the solution vector x.

[0155] In S201, the equality sign of option 10 represents the solution x of an invalid range. k Then, let A be the set of rows in Equation 10 where the equality sign is valid.e b e In S201, A e b e All are empty sets. Additionally, let A be the set of rows in Equation 10 where the equality sign is invalid. d b d In S201, A d =A, b d =b.

[0156] In S203, solve the following simultaneous equations, setting the solutions as x and λ. If x = x k Then proceed to S205. If x ≠ x k Then proceed to S207.

[0157] [Mathematical Expression 13]

[0158]

[0159] In S205, it is determined whether all elements of λ are 0 or higher. If they are 0 or higher, proceed to S213. If not all elements of λ are 0 or higher, proceed to S211.

[0160] In S207, α is obtained according to Equation 11 below. In Equation 10, b i a i They are from A d b d This is obtained by extracting one row from the previous row. If α = 1, proceed to S205. If α < 1, proceed to S209.

[0161] [Mathematical Expression 14]

[0162]

[0163]

[0164] In S209, the constraint used when α (<1) is calculated according to Equation 11 [b] i a i From A d b d Delete and append to A e b e And then enter S203.

[0165] In S211, the element with the smallest negative value λ is selected, and A is... e b e The constraints contained therein correspond to the constraints [b] i a i From A e b e Delete and append to Ad b d And then enter S203.

[0166] In S213, the solution x obtained in S203 is taken as the optimal solution and the process ends.

[0167] At once Figure 7 As shown in the effective constraint method, by using the additional multiplier λ to search for the combination of rows in Equation 10 where the equality sign is valid, it is possible to find the solution that satisfies Equation 10 and maximizes Equation 9.

[0168] [Application of the effective constraint method in the constrained optimization calculation unit 810]

[0169] Next, the application method of the effective constraint method in the constrained optimization calculation unit 810 of this embodiment will be explained.

[0170] In the comprehensive characteristic production unit 808, the predicted temperature column (predicted temperature vector) of the furnace temperature can be obtained in Equation 7, and the target temperature column (comprehensive target temperature vector) can be obtained in Equation 8. Therefore, in the constrained optimization calculation unit 810, the square of the error between the target temperature column and the predicted temperature column is used as the evaluation function. The evaluation function V(u(t)) becomes Equation 12 below.

[0171] [Mathematical Expression 15]

[0172]

[0173] If we compare the inside of the parentheses outside the second term of Equation 12 with Equation 9, then c and Q in Equation 9 can be replaced with the following expressions respectively.

[0174] [Mathematical Expression 16]

[0175] c = U dsr T ·[U tg -U zr ], Q = U dsr T ·U dsr

[0176] Therefore, by using the aforementioned effective constraint method, we can obtain the solution that maximizes the value inside the parentheses surrounding the second term of Equation 12. Thus, we can find the solution that minimizes the evaluation function V(u(t)) and the power supply value that minimizes the square of the error between the target temperature series and the predicted temperature series.

[0177] Next, regarding Equation 10 which involves constraints, if we use regions a to c from the first four terms as examples for the sake of simplicity, then as shown in Equation 13 below, the power supply value P for each region... a P bP c When assigning upper and lower limits to the left side of the arrow, an inequality can be established as shown on the right side of the arrow, thus applying it to Equation 10. In Equation 13 below, LLa and ULa are the upper and lower limits of the power supply value for region a, respectively; similarly, LLa, ULa, LLC, and ULC are the upper and lower limits of the power supply value for regions b and c, respectively. For example, LLa = 0% and ULa = 80%.

[0178] [Mathematical Expression 17]

[0179]

[0180] [Second Effective Restraint Method]

[0181] Next, the second effective constraint method that can be used in this disclosure will be explained. Regarding the above... Figure 7 Regarding the effective constraint method shown, when the CPU712's processing power is insufficient, it sometimes cannot complete the calculation within the predetermined control cycle. Therefore, it is possible to utilize... Figure 8 Replace Figure 7 The process is used to find the solution vector x.

[0182] and Figure 7 The difference between this and the first effective constraint method is that S215 is added after the initial step, changing the processing of S201 to S217, and setting it to enter the added S219 through S209 and S211, and entering S203 or S213 through the determination in S219. In the following text, only the differences from the first effective constraint method will be explained.

[0183] In S215, the loop count is initialized.

[0184] Then, in S217, the solution x of the range where the equality sign of equation 10 is invalid is selected. k To prevent the optimization calculation from ending prematurely in S219 (described later), specifically, the solution is set to the lower limit of the range where the equality sign in Equation 10 is invalid. For example, regarding the power supply value P of region a... a The constraint, in 0≤P a When (t)≤100, the choice solution is set to P. a (t) = 0.1, etc. By making such a choice, the constraints added in S209 take precedence over the lower constraint, so that even if the optimization calculation ends midway, a safe calculation result can be obtained.

[0185] In S219, the number of iterations is counted. If it is within the predetermined number, proceed to S203. If it exceeds the predetermined number, proceed to S213, take the solution x obtained in S203 as the optimal solution, and end.

[0186] By setting Figure 8 This process can complete the calculation of the optimal solution with the minimum required processing, and therefore can complete the calculation within the predetermined control cycle.

[0187] [Automatic acquisition steps for thermal properties]

[0188] Next, use Figure 9 The automatic acquisition steps of thermal characteristics using the temperature control unit 238 will be described. Through the automatic acquisition steps of thermal characteristics shown below, a predictive model required for control using the temperature control unit 238 is created and stored in the predictive model storage area 854.

[0189] First, when the automatic acquisition of thermal characteristics begins, a reference temperature for each furnace temperature is provided from the host controller 36. The temperature control unit 238 uses PID-based feedback control to control the furnace temperature in the following S300 and S302.

[0190] In S300, the furnace temperature is controlled by the temperature control unit 238, and this process is repeated until the furnace temperature rises or falls to near the reference temperature. At this time, the parameters used for control obtained from the parameter storage area 856 (e.g., PID parameters not shown) need to be asymptotically stable, but do not necessarily need to be optimal.

[0191] In step S302, the furnace temperature is controlled using the temperature control unit 238. This process is repeated until the furnace temperature is controlled to a reference temperature and reaches a stable state. At this time, the control parameters (e.g., PID parameters not shown) obtained from the parameter storage area 856 need to be asymptotically stable, but not necessarily optimal. When a stable state is determined, the current power supply value, or a certain time average of the power supply value, is written as a stable power value into the prediction model storage area 854. Additionally, when a stable state is determined, the current heater temperature, or a certain time average of the heater temperature, is written as a reference temperature for the heater temperature into the prediction model storage area 854. Furthermore, the reference temperature of the furnace temperature is written into the prediction model storage area 854.

[0192] In step S304, starting from the beginning of this step, only at preset times, the power supply unit 718 outputs random values ​​as power supply values ​​to the heater 206. Simultaneously, the current and past furnace temperatures and heater temperatures are obtained from the temperature history storage area 850, and the current and past power supply values ​​are obtained from the power supply value history storage area 852. Then, the furnace temperature prediction model is updated and stored using the obtained current and past furnace temperatures and power supply values. Similarly, the heater temperature prediction model is updated and stored using the obtained current and past heater temperatures and power supply values.

[0193] Here, the so-called random value refers to a 4-value discrete value centered on the stable power value stored in the prediction model storage area 854, which is randomly selected. Furthermore, the power supply value of one area is changed at a preset time interval (e.g., 1 minute). And, the area where the change occurs is randomly selected at a certain time. Updates to the prediction model will be discussed later.

[0194] In step S306, starting from the beginning of this step, the power supply unit 718 outputs a stable power value as a power supply value to the heater 206 only at preset times. Meanwhile, the current and past furnace temperatures and heater temperatures are obtained from the temperature history storage area 850, and the current and past power supply values ​​are obtained from the power supply value history storage area 852. Then, the furnace temperature prediction model is updated and stored using the obtained current and past furnace temperatures and power supply values. Similarly, the heater temperature prediction model is updated and stored using the obtained current and past heater temperatures and power supply values.

[0195] In S308, the same processing as in S304 is performed, except that the updated prediction model is evaluated. If the evaluation result determines that the prediction model is appropriate, proceed to S310. The evaluation of the prediction model will be described later.

[0196] In S310, the predicted model obtained in S308 is used, and the temperature control unit 238 is used to control the furnace temperature. This process is repeated until the furnace temperature is controlled to the reference temperature and reaches a stable state. When it is determined that a stable state has been reached, the stable power value, the reference temperature of the heater temperature, and the reference temperature are updated using the same method as in S302.

[0197] In S312, the same process as in S308 is performed. If the evaluation result indicates that the prediction model is appropriate, the automatic acquisition of thermal properties is terminated.

[0198] Figure 10 This is a processing block diagram showing the internal process of the temperature control unit 238 in steps S304, S308, and S312, which are automatic steps for acquiring thermal properties.

[0199] Figure 10 In this unit, the temperature control unit 238 includes a furnace temperature prediction model update unit 834, a prediction model evaluation unit 838, and a random power output unit 840. The most recently obtained values ​​for the reference temperature, stable power value, etc., involved in the prediction model are stored in the prediction model storage area 854.

[0200] First, as described in S304, the random power output unit 840 outputs a randomly selected value from four discrete values ​​centered on a stable power value to the limiter 708. Furthermore, as described later, the random power output units 840 exist in a number corresponding to the number of divisions of the heater 206, but as mentioned above, they cooperate with each other in a manner that changes the power supply value of a randomly selected area at preset time intervals (e.g., 1 minute).

[0201] Next, the furnace temperature prediction model update unit 834 obtains the prediction model of the furnace temperature in that area from the prediction model storage area 854, obtains the current and past data of the specified furnace temperature from the temperature history storage area 850, obtains the current and past data of the specified power supply value from the power supply value history storage area 852, calculates the latest prediction model of the furnace temperature at that point in time, and updates it.

[0202] The furnace temperature prediction model update unit 834 and the random power output unit 840 exist respectively with a number corresponding to the number of divisions of the heater 206, but Figure 10 The illustration is simplified and only one is shown.

[0203] Next, the prediction model evaluation unit 838 acquires a prediction model of the furnace temperature with a number of zone divisions at a preset evaluation interval (e.g., 10 minutes), and evaluates the acquired prediction model until the next acquisition time after the evaluation interval. The evaluation result determines whether the prediction model is appropriate or inappropriate.

[0204] [Methods for updating prediction models]

[0205] Next, in S304, S308, and S312 mentioned above, the following steps are taken: Figure 10 The method for updating the prediction model performed by the furnace temperature prediction model update unit 834 shown will be described. The update method in this disclosure uses a method called recursive least squares. Equation 27 below uses matrices and vectors to express Equation 1.

[0206] [Mathematical Expression 18]

[0207] Δy(t)=x T (t)·θ(t)...(Equation 27)

[0208]

[0209] Here, time t represents the current processing. The reason why the latest data in the elements of x(t) is y(t-1) is that, as mentioned above, the time of obtaining the temperature and power supply values ​​from this processing is set to t-1.

[0210] The coefficients θ(t) of the latest prediction model are calculated as follows, Equation 28.

[0211] [Mathematical Expression 19]

[0212] θ(t)=θ(t-1)+η(t)·k(t)...(Formula 28)

[0213]

[0214] η(t)=y(t-1)-x T (t-1)·θ(t-1)

[0215]

[0216] Here, y(t-1) is the temperature obtained in this study, and is the furnace temperature of the object in the prediction model. ρ is a parameter called the forgetting coefficient, and is obtained from parameter storage area 856. P(t) is the coefficient error correlation matrix, and is initialized with an identity matrix of, for example, elements from 100 to 1000.

[0217] Based on the input x(t), the θ(t) obtained in Equation 28 is sometimes clearly unsuitable for predicting temperature, or it may oscillate when used for control. Therefore, under the condition that conditions 1 to 4 related to the next model update are met, instead of following Equations 1 and 4 of Equation 28, the coefficient error correlation matrix P(t) and the coefficients θ(t) of the prediction model are made to be the same as before.

[0218] The first condition related to model updates is set to the case where the temperature of the object being predicted deviates from the baseline temperature (e.g., ±50°C).

[0219] The second condition related to model update is set to the factor of the coefficient θ(t) of the prediction model even if there is a deviation from the pre-defined range (e.g., -100 to +100).

[0220] The third condition related to model update is set as ma1(t), ..., ma among the elements of the coefficients θ(t) of the prediction model. n(t), mb1(t), ...mb n (t), ..., me n The case where the sum of (t) is negative.

[0221] The fourth condition related to model updates is set as the case where the following transfer function, consisting of a1(t) and a2(t) among the elements of the coefficients θ(t) of the prediction model, is unstable.

[0222] [Mathematical Expression 20]

[0223]

[0224] However, when the number of calculations in Equation 28 is small, the first to fourth conditions related to model updates may be met consecutively based on the input x(t). If this happens, the predictive model will never achieve the desired accuracy. Therefore, the coefficients θ(t) of the predictive model can be updated only a predetermined number of times, ignoring the first to fourth conditions related to model updates.

[0225] If the coefficients θ(t) of the prediction model obtained in Equation 28 do not meet any of the conditions in the first to fourth conditions mentioned above, they are stored together with the coefficient error correlation matrix P(t) in the prediction model storage area 854.

[0226] If the evaluation results in S304, S308, and S312 above are appropriate, then the coefficients θ(t) of the prediction model are determined, and by... Figure 6 The individual characteristics shown are read out and used by the manufacturing unit 804, etc.

[0227] [Evaluation methods for prediction models]

[0228] The following describes the use of S304, S308, and S312 mentioned above. Figure 10 The evaluation method of the prediction model performed by the prediction model evaluation unit 838 shown will be explained.

[0229] A predictive model of furnace temperature is obtained at a pre-set evaluation interval (e.g., 10 minutes), and the obtained predictive model is evaluated until the next evaluation period. The obtained predictive model is deemed appropriate when all of the following conditions 1 to 3, which are related to the evaluation method, are met.

[0230] The first condition related to the evaluation method is that all prediction models do not meet any of the first to fourth conditions related to model updates.

[0231] The second condition related to the evaluation method is set as follows: taking all prediction models as the object, the sum of the changes C of the prediction model coefficients obtained by Equation 29 at all times when the prediction model is updated.vg The values ​​of (t) are calculated and their maximum values ​​are below the pre-set convergence criteria.

[0232] [Mathematical Expression 21]

[0233] Cvg(t)=[θ(t)-θ(t-1)] T ·[θ(t)-θ(t-1)]...(Equation 29)

[0234] The third condition related to the evaluation method is set as follows: taking all prediction models as the object, the prediction errors obtained using the prediction models are calculated at all processing times within the evaluation interval, and these errors are below a pre-set error judgment value. The prediction error E in the evaluation method... pe (t) is calculated as shown in Equation 30 below.

[0235] [Mathematical Expression 22]

[0236] E pe (t)=y(t-1)-Δy(t-1)...(Formula 30)

[0237] Δy(t-1)=x T (t-1)·θ

[0238]

[0239] For the coefficients θ of the prediction model in Equation 30, they are obtained in the initial processing of the evaluation interval and remain unchanged until the next processing in subsequent evaluation intervals, therefore they are set as constants. Furthermore, the input x(t) is set as...

[0240] [Mathematical Expression 23]

[0241]

[0242] In the next second processing, set to

[0243] [Mathematical Expression 24]

[0244]

[0245] In the subsequent third and subsequent processing steps, set as

[0246] [Mathematical Expression 25]

[0247]

[0248] That is, at the initial processing time when the prediction model is obtained for evaluation, the past and current measured temperatures obtained from the temperature history storage area 850 are used for the past temperatures as prediction materials, but in subsequent processing, the prediction temperatures calculated in the previous processing are used.

[0249] Next, use Figure 11 (A) and Figure 11 (B) will be described as follows: A method for performing oxidation, diffusion, and other treatments on a wafer 200 using the processing furnace 202 of the substrate processing apparatus described above as a substrate processing step in the manufacturing process of a semiconductor device. It should be noted that, in the following description, the operation of each part constituting the substrate processing apparatus is controlled by the main control unit 240.

[0250] (Step S101)

[0251] First, multiple wafers 200 are loaded (wafer filling) into the wafer boat 217. Then, the temperature is maintained at the target temperature T0 in the processing chamber 201. At this time, the power supply to the heater 206 is controlled by feedback based on the temperature information detected by the first temperature sensor 263 and the second temperature sensor 264, so that the processing chamber 201 achieves the desired temperature distribution.

[0252] (Step S102)

[0253] Next, as Figure 1 As shown, a crystal boat 217 holding multiple wafers 200 is lifted by a crystal boat lift 115 and moved into a processing chamber 201, which serves as a furnace (crystal boat loading, substrate transfer). In this state, the sealing cap 219 seals the lower end of the reaction tube 204 via a base 257 and an O-ring 220. At this time, the heater 206 is heated by the temperature control unit 238 to achieve a target temperature T0 in the processing chamber 201. Additionally, the exhaust device 246 exhausts gas to achieve a desired pressure in the processing chamber 201. The pressure in the processing chamber 201 is measured by a pressure sensor 245, and the pressure regulator 242 is controlled based on this measured pressure. Next, the heat insulation cylinder 218 and the crystal boat 217 are rotated by a rotating mechanism 254, thereby rotating the wafers 200.

[0254] (Step S103)

[0255] After the processing chamber 201 is maintained at the processing temperature T0, gas supplied from the processing gas supply source and the carrier gas supply source, and controlled by the MFC 241 at the desired flow rate, flows from the gas supply pipe 232 through the gas inlet 230 and the capillary tube 234 to the top 233, and is then introduced into the processing chamber 201 in a cluster pattern from multiple gas inlets 233a. The introduced gas flows down in the processing chamber 201, flows through the exhaust port 231a, and is exhausted from the gas exhaust section 231. As the gas passes through the processing chamber 201, it contacts the surface of the wafer 200, performing processes such as oxidation and diffusion on the wafer 200.

[0256] (Step S104)

[0257] If the preset processing time has elapsed, inert gas is supplied from the inert gas supply source, and the processing chamber 201 is replaced with inert gas, and the pressure in the processing chamber 201 returns to atmospheric pressure. Then, the sealing cover 219 is lowered using the crystal boat lift 115, the lower end of the reaction tube 204 is opened, and the processed wafer 200, while held in the crystal boat 217, is removed from the lower end of the reaction tube 204 from inside the furnace to outside the reaction tube 204 (crystal boat unloading, substrate removal). Then, the processed wafer 200 is removed from the crystal boat 217 (wafer removal).

[0258] like Figure 11 As shown in (B), even though the furnace temperature, which serves as the temperature of the processing chamber 201, is raised and maintained at the target temperature T0 in step S101, the furnace temperature is temporarily lower than T0 because the atmosphere outside the furnace is introduced into the furnace when the wafer held in the crystal boat 217 is moved into the processing chamber 201 during crystal boat loading (step S102). Then, the furnace temperature stabilizes again at the target temperature T0, and processing is performed after maintaining it at T0 (step S103). However, how to shorten the recovery temperature becomes a problem. The recovery temperature is the temperature at which the furnace temperature quickly converges to the target temperature T0, which serves as the processing temperature.

[0259] For example, in the crystal boat loading (step S102) described above, by using the temperature control unit 238, the temperature control unit 238 controls the power supply to the heater so that the predicted temperature series calculated based on the pre-held furnace temperature prediction model is close to the future target temperature series, thereby causing the furnace temperature to converge towards the target temperature T0 and shortening the recovery time from crystal boat loading (step S102) to processing (step S103). Furthermore, the temperature control unit 238 can also be used in the crystal boat unloading (step S104).

[0260] Figure 12This diagram illustrates the processing of the target temperature calculation unit 870 when the temperature control unit 238 described above is used in the case of loading the crystal boat (step S102).

[0261] like Figure 12 As shown, after the furnace temperature is maintained at the target temperature T0 in step S101, the wafer loading begins at time t0 (step S102). The final target temperature in step S102 is set to T1. Furthermore, as the wafer is placed into the furnace, the furnace temperature decreases from T0.

[0262] At this time, with the ramp rate control described above used, the current target temperature, the final target temperature, and the ramp rate are provided to the target temperature calculation unit 870 after time t0. During each control cycle, such as at times t1 and t2, the current target temperature, the final target temperature, and the ramp rate are calculated. Figure 12 The target temperature of the triangle marker (△) shown is set to S. tg (t+1), along the dashed line calculated based on the slope and the final target temperature, calculate the target temperature column vector S. tg .

[0263] In contrast, during a pre-set period, such as when overshoot is likely to occur (e.g., during crystal boat loading (step S102) or crystal boat unloading (step S104), the aforementioned temperature convergence ramp rate is provided to the target temperature calculation unit 870 at a time after t0. Then, at each time point in each control cycle, such as t1 or t2, the temperature convergence ramp rate is... Figure 12 The current furnace temperature indicated by the four corner marks (□) is set to S. tg (t+1), along the solid line calculated using the slope and the final target temperature based on temperature convergence, calculate the target temperature column vector S. tg That is, during a preset period, the target temperature calculation unit 870 updates the future target temperature series according to the current temperature, the final target temperature, and the temperature convergence slope. This suppresses overshoot and enables the furnace temperature to converge rapidly to the target temperature.

[0264] [Second Embodiment of this Disclosure Text]

[0265] Next, the second embodiment of this disclosure will be described.

[0266] Figure 13 For use with the temperature control unit according to the second embodiment of this disclosure. Figure 11 The diagram illustrates the process in step S102 of (A).

[0267] In the second embodiment of this disclosure, a target temperature column calculation unit 872 is used instead of the target temperature column calculation unit 870 described above.

[0268] Regarding the target temperature column calculation unit 872, the target temperature is input from the host controller 36 via the input terminal S, and the furnace temperature is input from the input terminal F to calculate the target temperature column vector S. tg .

[0269] Regarding the target temperature column calculation unit 872, in addition to the target temperature, the final target temperature and the ramp rate are provided from the input terminal S at a certain control cycle. Furthermore, the host controller 36 provides the target temperature column calculation unit 872 with a specified temperature convergence time at any time. The specified temperature convergence time refers to the value used to calculate the proportion of change so that the final target temperature is reached after a specified time when the current furnace temperature changes from the current target temperature to the final target temperature. For example, if it is set to 10 minutes, the target temperature column vector S that changes the current furnace temperature to the final target temperature is calculated such that the final target temperature is reached 10 minutes after the time input from the host controller 36. tg The target temperature column calculation unit 872 calculates the target temperature column vector S, which is the future target temperature column, based on the current furnace temperature (as the current temperature), the final target temperature, and the specified time for temperature convergence. tg Update.

[0270] For example, the target temperature column calculation unit 872 has an internal counter that starts when the provided temperature converges to a specified time, and calculates the target temperature column vector S based on the count value, the current furnace temperature, and the final target temperature. tg Target temperature column vector S tg The number of rows corresponding to the number of furnace temperatures (region divisions) that are controlled objects is calculated, and the number of rows corresponds to the number of rows in Equation 4.

[0271] Figure 13 In, also with Figure 12 Similarly, after the furnace temperature is maintained at the target temperature T0 in step S101, the wafer loading begins at time t0 (step S102). The final target temperature in step S102 is set to T1. Furthermore, as the wafer is placed into the furnace, the furnace temperature decreases from T0.

[0272] At this time, with the ramp rate control described above used, the current target temperature, the final target temperature, and the ramp rate are provided to the target temperature calculation unit 872 after time t0. During each control cycle, such as at times t1 and t2, the current target temperature, the final target temperature, and the ramp rate are calculated. Figure 13 The target temperature of the triangle marker (△) shown is set to S. tg (t+1), along the dashed line calculated based on the slope and the final target temperature, calculate the target temperature column vector S. tg .

[0273] In contrast, during a pre-set period, such as when overshoot is likely to occur (e.g., during crystal boat loading (step S102) or crystal boat unloading (step S104), the aforementioned temperature convergence specified time is provided to the target temperature calculation unit 872 at time t0. Then, at each time point in each control cycle, such as t1 or t2, the temperature convergence specified time is... Figure 13 The current furnace temperature indicated by the four corner marks (□) is set to S. tg (t+1), along the solid line calculated from the remaining time until the specified temperature convergence time and the final target temperature, calculate the target temperature column vector S. tg Therefore, over-adjustment can be suppressed, and the furnace temperature can be quickly converged to the target temperature.

[0274] [Third Embodiment of This Disclosure Text]

[0275] Next, the third embodiment of this disclosure will be described.

[0276] Figure 14 For use with the temperature control unit according to the third embodiment of this disclosure. Figure 11 The diagram illustrates the process in step S102 of (A).

[0277] In the third embodiment of this disclosure, a target temperature column calculation unit 874 is used instead of the target temperature column calculation unit 870 described above.

[0278] Regarding the target temperature column calculation unit 874, the target temperature is input from the host controller 36 via the input terminal S, and the furnace temperature is input from the input terminal F to calculate the target temperature column vector S. tg .

[0279] Regarding the target temperature column calculation unit 874, in addition to the target temperature, the final target temperature and the ramp rate are provided from the input terminal S at a certain control cycle. Furthermore, the host controller 36 provides the target temperature column calculation unit 874 with a specified temperature convergence time and a specified reference region at any time. The specified temperature convergence time refers to the value used to calculate the ratio of change when the current target temperature changes from the current furnace temperature to the final target temperature, so that the final target temperature is reached after a specified time. The specified reference region refers to the region within the target temperature column calculation unit 874 that specifies the calculated target temperature column vector S. tgThe current furnace temperature range. For example, if the specified temperature convergence time is set to 10 minutes and the specified reference range is set to range a, then the target temperature column vector S from the current furnace temperature in range a to the final target temperature is calculated in such a way that the final target temperature is reached 10 minutes after the input from the upper controller 36. tg That is, the current furnace temperature is replaced with the current furnace temperature of the specified reference region. Then, the target temperature column vector S is calculated from the specified reference region in such a way that the temperature converges to the final target temperature within a specified time. tg That is, the target temperature calculation unit 874 updates the future target temperature column according to the current temperature, the final target temperature, and the specified temperature convergence time.

[0280] Figure 14 In, also with Figure 12 Similarly, after the furnace temperature is maintained at the target temperature T0 in step S101, wafer loading begins at time t0 (step S102). The final target temperature in step S102 is set to T1. Furthermore, as the wafer is placed into the furnace, the furnace temperature decreases from T0. Figure 14 The image shows the furnace temperature measured by thermocouple 263a in region a and the furnace temperature measured by thermocouple 263b in region b.

[0281] At this point, with the aforementioned ramp rate control in place, the current target temperature, final target temperature, and ramp rate are provided to the target temperature calculation unit 874 after time t0. At each control cycle, such as t1 and t2, the current target temperature, final target temperature, and ramp rate are calculated. Figure 14 The target temperature of the triangle marker (△) shown is set to S. tg (t+1), calculate the target temperature column vector S along the dashed line calculated based on the slope and the final target temperature. tg .

[0282] In contrast, during a pre-set period, such as when overshoot is likely to occur (e.g., during crystal boat loading (step S102) or crystal boat unloading (step S104), the aforementioned temperature convergence specified time is provided to the target temperature calculation unit 874 at time t0. Then, at each time point in each control cycle, such as t1 or t2, the temperature convergence specified time is... Figure 14 The current furnace temperature indicated by the four corner marks (□) is set to S. tg (t+1), along the solid line calculated from the remaining time until the specified temperature convergence time and the final target temperature, calculate the target temperature column vector S. tg For example, with region a as the reference area, the target temperature column vector S, representing the change in furnace temperature from the current temperature in region a to the final target temperature, is calculated. tgFurthermore, for regions such as region b, the target temperature column vector S is also calculated based on the current furnace temperature in region a. tg Therefore, over-adjustment can be suppressed, and the furnace temperature can be quickly converged to the target temperature.

[0283] Example

[0284] Next, the embodiments will be described.

[0285] Temperature control based on the comparative example and this embodiment is used respectively to bring the furnace temperature in the above-mentioned crystal boat loading (step S102) to converge to the target temperature. Figure 15 Temperature trajectories for each region are based on temperature control using the slope ratio described in the comparative example. Additionally, Figure 16 (A) is the temperature trajectory in each region based on the temperature control of the target temperature calculation unit 874 described above in this embodiment. Figure 16 (B) represents the temperature trajectory in each region based on the temperature control of the target temperature calculation unit 874 described above in this embodiment. Figure 16 In (B), the number of chips in the processing chamber is set to Figure 16 Temperature control is performed by using half the number of chips in (A).

[0286] like Figure 15 As shown, it was confirmed that over-adjustment occurred in the temperature control using the slope ratio involved in the comparative example, and the temperature of each zone was controlled sporadically. Furthermore, it was confirmed that the recovery temperature was prolonged.

[0287] In contrast, such as Figure 16 As shown in (A), it was confirmed that by performing temperature control using the target temperature calculation unit 874 of this disclosure, overshoot can be suppressed and the inter-regional deviation of each region can be reduced. Furthermore, it was confirmed that compared to the comparative example, it can converge to the target temperature more quickly, thereby shortening the recovery time. Additionally, as... Figure 16 As shown in (B), it can be confirmed that even if the number of wafers moved into the processing chamber is halved, which causes a change in the heating and cooling characteristics of the wafers themselves, over-adjustment can still be suppressed.

[0288] As explained in detail above, the temperature control unit 238 of this embodiment can suppress overshoot and quickly converge the furnace temperature towards the target temperature, thereby reducing the deviation between regions. Furthermore, even when the temperature characteristics of the individual heaters deviate significantly, or when the responsible engineer has insufficient time, the thermal characteristics can be automatically obtained, enabling the acquisition of the optimal control method without parameter adjustments or with easy parameter adjustments. Therefore, the desired device performance can be easily obtained.

[0289] The above describes in detail the implementation methods of this disclosure, but this disclosure is not limited to the above implementation methods and embodiments, and various changes can be made without departing from its spirit.

[0290] Furthermore, while the above embodiments describe examples of oxidation or diffusion treatment on wafer 200, this disclosure is not limited to these methods. For example, film formation processes such as CVD can also be used, and the type of film is not particularly limited. For example, it can be appropriately applied when various types of films, such as SiN films and metal oxide films, are formed on wafer 200. In addition, it can certainly be applied to various processes such as annealing and epitaxial growth (Epi).

[0291] Furthermore, it can be applied not only to semiconductor manufacturing apparatuses that process semiconductor wafers, such as the substrate processing apparatus described in the above embodiments, but also to LCD (Liquid Crystal Display) manufacturing apparatuses that process glass substrates.

[0292] Explanation of reference numerals in the attached figures

[0293] 200 wafers (substrates)

[0294] 206 Heater

[0295] 238 Temperature Control Department

Claims

1. A substrate processing method, comprising: The substrate loading process involves loading multiple substrates held in a substrate holder into the processing chamber. A substrate processing step, which processes the substrate; The process includes a substrate removal step, which removes the substrate from the processing chamber; and a step of controlling the power supply to the current heater in a manner that makes the predicted temperature series calculated according to a pre-held prediction model approach the future target temperature series, wherein... In the substrate loading process, the future target temperature series is updated based on the current temperature, the final target temperature, and the temperature convergence ramp rate, where the temperature convergence ramp rate is the ratio of the change from the current temperature (i.e., the current furnace temperature) to the final target temperature.

2. The substrate processing method as described in claim 1, wherein, When updating the future target temperature column, the current temperature is replaced with the current temperature of the specified reference area and applied.

3. The substrate processing method as described in claim 1, wherein, Calculate: an individual input response characteristic matrix, which represents the amount of change in the predicted temperature vector, which is represented in vector form as the predicted temperature column, due to the influence of the calculated power supply value; and an individual zero response characteristic vector, which represents the amount of change in the predicted temperature vector due to the influence of past furnace temperatures and past power supply values.

4. The substrate processing method as described in claim 3, further comprising: The process of creating a comprehensive characteristic equation using the individual input response characteristic matrix, the individual zero response characteristic vector, and the target temperature column vector representing the future target temperature column in vector form; and The process involves inputting the integrated input response characteristic matrix, integrated zero response characteristic vector, integrated target temperature vector, and upper and lower limits for each region, calculated by the process of creating the integrated characteristic equation, and then using the effective constraint method to calculate the current power supply value based on the integrated characteristic equation.

5. The substrate processing method as described in claim 1, wherein, The prediction model includes coefficients, a coefficient error correlation matrix, a reference temperature, and a stable power value for predicting at least one of the heater temperature and the furnace temperature.

6. The substrate processing method as described in claim 5, wherein, At least one of the group consisting of the coefficients involved in the prediction model, the coefficient error correlation matrix, the reference temperature, and the stable power value is selected and defined separately according to the heater temperature of each region and the furnace temperature of each region.

7. The substrate processing method as described in claim 5, wherein, For prediction models related to heater temperatures and furnace temperatures in all regions, all of the above are grouped together as one, corresponding to each temperature zone.

8. The substrate processing method as described in claim 5, wherein, The prediction model is represented by the following Equation 1, which calculates the predicted temperature inside the furnace. [Mathematical Expression 1] Here, Δy(t) represents the deviation of the predicted temperature from the reference temperature at time t, y(t-1) and y(t-2) represent the deviations of the temperatures 1 and 2 times prior from the reference temperature, respectively, and p a (t-1), p a (t-2), ..., p a (tn) represents the deviation of the power supply value from the stable power value in region a 1st, 2nd, ..., nth time ago, p b (t-1), p b (t-2), ..., p b (tn) represents the deviation of the power supply value of region b from the stable power value before the 1st, 2nd, ..., nth time, p c (t-1), p c (t-2), ..., p c (tn) represents the deviation of the power supply value from the stable power value in region c before the 1st, 2nd, ..., nth time iterations, and p d (t-1), p d (t-2), ..., p d (tn) represents the deviation of the power supply value from the stable power value in region d before the 1st, 2nd, ..., nth time iterations, and p e (t-1), p e (t-2), ..., p e (tn) represents the deviation of the power supply value of region e from the stable power value 1, 2, ..., nth time ago, where a1, a2, ma1, ..., ma n mb1, ..., mb n ,mc1, ...,mc n md1, ..., md n me1, ..., me n , where bi is the coefficient; bi is the constant term; and n is the value set among various parameters.

9. The substrate processing method as described in claim 5, wherein, The prediction model is represented by the following Equation 2, which calculates the predicted temperature of the heater. [Mathematical Expression 2] Here, Δy h (t) represents the deviation of the predicted heater temperature from the reference temperature at time t, where y is the temperature at time t. h (t-1), y h (t-2) represents the deviation of the heater temperature from the reference temperature before the first and second cycles, p(t-1), p(t-2), ..., p(tn) represent the deviation of the power supply value from the stable power value in the corresponding region before the first, second, ..., n cycles, and a1, a2, m1, m2, ..., m n Each of these represents a coefficient, bi is a constant term, and n is a value pre-set as various parameters.

10. The substrate processing method as described in claim 4, wherein, The comprehensive characteristic equations are represented by the following equations 7 and 8. [Mathematical Expression 3] Here, U dsr U represents the comprehensive input-response characteristic matrix. zr U represents the vector of the comprehensive zero response characteristics. tg Let Δy represent the combined target temperature vector. a (t), ..., Δy e (t) is the predicted temperature vector corresponding to regions a, ..., e, S zr-a S zr-e S represents the individual zero-response characteristic vectors corresponding to regions a, ..., and e. dsr-a S dsr-e S is the individual input response characteristic matrix corresponding to regions a, ..., and e. tg-a S tg-e Let u(t) be the target temperature column vector corresponding to region a, ..., region e, and let Ncd be the power supply value at time t. Let Ncd be the number of input rows held in the first stage. The input u(t) of the first stage is held until time t+Ncd-1, and the input of the second stage is held as u(t+Ncd) thereafter.

11. The substrate processing method as described in claim 4, wherein, The comprehensive characteristic equation includes a predicted temperature series for the furnace temperature and a target temperature series for the furnace temperature.

12. The substrate processing method as described in claim 4, wherein, The comprehensive characteristic equation is constructed by finding the solution vector x that maximizes the evaluation function f, as expressed by the following equations 9 and 10. [Mathematical Expression 4] Here, c, Q, b, and A are the provided constant matrices or vectors; in addition, T denotes transpose.

13. The substrate processing method as described in claim 12, wherein, The evaluation function f is constructed in a way that minimizes the square of the error between the target temperature series and the predicted temperature series.

14. A method for manufacturing a semiconductor device, comprising: The substrate loading process involves loading multiple substrates held in a substrate holder into the processing chamber. A substrate processing step, which processes the substrate; The process includes a substrate removal step, which removes the substrate from the processing chamber; and a step of controlling the power supply to the current heater in a manner that makes the predicted temperature series calculated according to a pre-held prediction model approach the future target temperature series. In the substrate loading process, the future target temperature series is updated based on the current temperature, the final target temperature, and the temperature convergence ramp rate, where the temperature convergence ramp rate is the ratio of the change from the current temperature (i.e., the current furnace temperature) to the final target temperature.

15. A computer-readable recording medium having a program that causes a substrate processing apparatus to perform the following steps: a substrate loading step, which loads multiple substrates held in a substrate holder into a processing chamber. A substrate processing step, which processes the substrate; The steps include a substrate removal step, which removes the substrate from the processing chamber; and a step of controlling the power supply to the current heater in a manner that brings the predicted temperature series calculated according to a pre-maintained prediction model close to the future target temperature series. In the substrate loading step, the program performs a step of updating the future target temperature column based on the current temperature, the final target temperature, and the temperature convergence ramp rate, wherein the temperature convergence ramp rate is the ratio of the change from the current temperature (i.e., the current furnace temperature) to the final target temperature.

16. A substrate processing apparatus, comprising: A heater is disposed outside the reaction tube and heats the substrate held in the substrate holder; A temperature history region that stores temperature data for at least one of the heater temperature and the furnace temperature. A prediction model storage area for storing temperature data of at least one of the heater temperature and the furnace temperature; The control unit is configured to perform the following process: substrate transfer process, which transfers multiple substrates held in a substrate holder into the processing chamber. Substrate processing, which processes the substrate; Substrate removal process, which removes the substrate from the processing chamber; as well as The temperature control unit is configured to control the power supply to the heater in a manner that makes the predicted temperature series calculated according to the prediction model approach the future target temperature series. In the substrate loading process, the future target temperature series is updated based on the current temperature, the final target temperature, and the temperature convergence ramp rate, where the temperature convergence ramp rate is the ratio of the change from the current temperature (i.e., the current furnace temperature) to the final target temperature.

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