Substrate processing device, temperature control method, method for manufacturing semiconductor device, and temperature control program

Abstract

Provided is a technology for controlling the supply of power to a current heater so that a predicted temperature series calculated in accordance with a prediction model retained in advance approximates a future target temperature series, wherein the predicted temperature series is updated in accordance with an error between a current measured temperature, which is a temperature measured most recently, and a current predicted temperature, which is calculated on the basis of the predicted temperature series and a past temperature, which is a temperature measured in the past.

Description

Substrate processing apparatus, temperature control method, semiconductor device manufacturing method, and temperature control program

[0001] This disclosure relates to a substrate processing apparatus, a temperature control method, a semiconductor device manufacturing method, and a temperature control program.

[0002] In semiconductor manufacturing equipment, for example, a substrate is placed in a furnace to form a thin film on a processing substrate, and the furnace is heated. To maintain the furnace at an appropriate temperature or to make the furnace follow a specified temperature change, temperature control is performed using feedback control based on proportional-integral-differential (PID) calculations, based on a preset temperature. On the other hand, in recent years, temperature control that does not use PID calculations has been implemented, as described in Japanese Patent Publication No. 2019-145730, International Publication No. 2022-064713, and International Publication No. 2022-070310.

[0003] This disclosure provides a technology that maintains high temperature control performance within a furnace.

[0004] According to one aspect of this disclosure, a technique is provided for controlling the power supplied to a heater so that a predicted temperature sequence calculated according to a pre-held prediction model approaches a future target temperature sequence, wherein the predicted temperature sequence is updated according to the prediction error between the current measured temperature (the temperature measured this time), the past measured temperature (the temperature measured in the past), and the past predicted current temperature calculated based on the predicted temperature sequence.

[0005] According to this disclosure, temperature control can be performed in such a way that high temperature control performance is maintained inside the furnace.

[0006] This is a longitudinal cross-sectional view showing a processing furnace of a substrate processing apparatus according to one embodiment of the present disclosure. This is a schematic diagram showing an example of a configuration in which the heater temperature is controlled by a temperature control unit according to one embodiment of the present disclosure. This is a block diagram showing the control configuration of a temperature control unit according to one embodiment of the present disclosure. This is a diagram showing an example of data stored in the prediction model storage area shown in Figure 3, which is a reference value for the prediction model of the heater temperature of zone a, and shows the amount of power supplied for each zone when the heater temperature of zone a is in a steady state at the reference temperature, with the reference temperature set to 101°C. This is a diagram showing an example of data stored in the prediction model storage area shown in Figure 3, which is a reference value for the prediction model of the heater temperature of zone b, and shows the amount of power supplied for each zone when the heater temperature of zone b is in a steady state at the reference temperature, with the reference temperature set to 111°C. This is a diagram showing an example of data stored in the prediction model storage area shown in Figure 3, which is a reference value for the prediction model of the furnace temperature of zone a, and shows the amount of power supplied for each zone when the furnace temperature of zone a is in a steady state at the reference temperature, with the reference temperature set to 202°C. This figure shows an example of data stored in the prediction model memory area shown in Figure 3, which is a reference value for the prediction model of the furnace temperature in zone b, and shows the amount of power supplied for each zone when the furnace temperature in zone b is in a steady state at the reference temperature, with the reference temperature set to 212°C. This figure shows another example of data stored in the prediction model memory area shown in Figure 3. This is a control block diagram of the inside of the temperature control unit according to one embodiment of the present disclosure. This is a flowchart explaining the first effective constraint method used in the present disclosure. This is a flowchart explaining the second effective constraint method used in the present disclosure. This is a control block diagram of the inside of the temperature control unit according to a modified example of one embodiment of the present disclosure. This is a flowchart showing an example of a substrate processing process. This figure shows the change in furnace temperature in each processing step of Figure 10A. This figure shows an example of the processing of the integrated characteristics creation unit when the temperature control unit is used in the substrate processing process shown in Figure 10A, and is an image diagram that calculates a predicted temperature sequence when a constant steady power value is output from past temperatures and a previously acquired temperature characteristic model.This figure shows an example illustrating the processing of the integrated characteristics creation unit when a temperature control unit is used in the substrate processing process shown in Figure 10A, and is an illustrative diagram showing how the difference between the calculated current predicted temperature (current predicted temperature) and the measured temperature is calculated as the prediction error. This figure shows an example illustrating the processing of the integrated characteristics creation unit when a temperature control unit is used in the substrate processing process shown in Figure 10A, and is an illustrative diagram showing how the predicted temperature sequence is corrected using the prediction error regardless of the magnitude of the deviation. This is a flowchart showing a first example of the procedure for automatically acquiring thermal characteristics of a temperature control unit according to one embodiment of this disclosure. This is a control block diagram of the inside of the temperature control unit in S308 and S312 shown in Figure 12.

[0007] <An Embodiment of the Present Disclosure> An embodiment of the present disclosure is described below. The drawings used in the following description are all schematic, and the dimensional relationships and ratios of the elements shown in the drawings do not necessarily correspond to those of reality. Furthermore, the dimensional relationships and ratios of the elements do not necessarily correspond between multiple drawings.

[0008] Figure 1 is a schematic diagram of a processing furnace 202 of a substrate processing apparatus used in the manufacture of a semiconductor device according to one embodiment of the present disclosure, and is shown as a vertical cross-sectional view.

[0009] As shown in Figure 1, the processing furnace 202 has a heater 206 as a heating mechanism. The heater 206 is cylindrical and is mounted vertically by being supported by a heater base 251 which serves as a holding plate.

[0010] Inside the heater 206, a heat-sensing tube (outer tube) 205, which is cylindrical in shape with a closed upper end and an open lower end, is arranged concentrically with the heater 206. Inside the heat-sensing tube 205, a reaction tube (inner tube) 204, which is cylindrical in shape with a closed upper end and an open lower end, is arranged concentrically with the heat-sensing tube 205, and is made of a heat-resistant material such as quartz (SiO2). A processing chamber 201 is formed in the hollow cylindrical portion of the reaction tube 204, and is configured to accommodate wafers 200 as substrates in a horizontal position, aligned vertically in multiple stages by a boat 217, which will be described later.

[0011] A gas inlet 230 is provided at the lower end of the reaction tube 204, and a thin tube 234 serving as a gas inlet is arranged along the outer wall of the reaction tube 204 from the gas inlet 230 to the ceiling 233 of the reaction tube 204. The gas introduced from the gas inlet 230 flows through the thin tube 234 to the ceiling 233, and is introduced into the processing chamber 201 from a plurality of gas inlets 233a provided in the ceiling 233. In addition, a gas exhaust section 231 is provided at a different location from the gas inlet 230 at the lower end of the reaction tube 204, to exhaust the atmosphere inside the reaction tube 204 from an exhaust port 231a.

[0012] A gas supply pipe 232 is connected to the gas inlet 230. On the upstream side of the gas supply pipe 232, opposite to the connection side with the gas inlet 230, a mass flow controller (MFC) 241 is connected to a processing gas supply source, a carrier gas supply source, and an inert gas supply source (not shown). A gas flow control unit 235 is electrically connected to the MFC 241 and is configured to control the flow rate of the supplied gas at a desired timing so that it reaches a desired amount.

[0013] 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 side connected to the gas exhaust section 231, an exhaust device 246 is connected via a pressure sensor 245 and a pressure regulator 242, which are configured to exhaust gas so that the pressure in the processing chamber 20 reaches a predetermined pressure. A pressure control unit 236 is electrically connected to the pressure regulator 242 and the pressure sensor 245, and the pressure control unit 236 is configured to control the pressure regulator 242 at a desired timing so that the pressure in the processing chamber 201 reaches a desired pressure based on the pressure detected by the pressure sensor 245.

[0014] At the lower end of the reaction tube 204, a base 257 is provided as a holder capable of airtightly closing the lower end opening of the reaction tube 204, and a seal cap 219 is provided as a furnace opening cover. The seal cap 219 is made of a metal such as stainless steel and is formed in the shape of a disc. The base 257 is made of a metal such as quartz and is formed in the shape of a disc, and is mounted on top of the seal cap 219. An O-ring 220 is provided on the upper surface of the base 257 as a sealing member that contacts the lower end of the reaction tube 204. On the side of the seal cap 219 opposite the processing chamber 201, a rotating mechanism 254 for rotating the boat 217 is installed. The rotating shaft 255 of the rotating mechanism 254 passes through the seal cap 219 and the base 257 and is connected to the insulating cylinder 218 and the boat 217, and is configured to rotate the wafer 200 by rotating the insulating cylinder 218 and the boat 217. The seal cap 219 is configured to move vertically up and down by a boat elevator 115, which is a lifting mechanism installed vertically outside the reaction tube 204, thereby enabling the boat 217 to be loaded into and unloaded from the processing chamber 201. The rotation mechanism 254 and the boat elevator 115 are electrically connected to a drive control unit 237, which is configured to control them at the desired timing to perform the desired operation.

[0015] The boat 217, which serves 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 position with their centers aligned. Below the boat 217, a cylindrical insulating tube 218, which serves as an insulating member made of a heat-resistant material such as quartz or silicon carbide, is provided to support the boat 217, and is configured to prevent heat from the heater 206 from being transferred to the lower end of the reaction tube 204.

[0016] The processing furnace 202 is equipped with two types of sensors as temperature detectors. Specifically, a first temperature sensor 263 is installed between the reaction tube 204 and the heat equalization tube 205. A second temperature sensor 264 is installed between the heat equalization tube 205 and the heater 206. The first temperature sensor 263 and the second temperature sensor 264 each detect temperature using multiple thermocouples. Details of the first temperature sensor 263 and the second temperature sensor 264 will be described later. The heater 206, the first temperature sensor 263, and the second temperature sensor 264 are electrically connected to a temperature control unit 238.

[0017] The gas flow control unit 235, pressure control unit 236, drive control unit 237, temperature control unit 238, and operation unit 239 are configured as the main control unit 240. The operation unit 239 is equipped with input / output units and display units (not shown) 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. A higher-level controller 36 is also connected to the main control unit 240. The higher-level controller 36 is configured with input / output units and the like, similar to the operation unit 239, and may be configured so that the main control unit 240 is controlled based on the higher-level controller 36.

[0018] Next, a method for processing a wafer 200 as one step in the semiconductor device manufacturing process will be described using the processing furnace 202 according to the above configuration. In the following description, the operation of each part constituting the substrate processing apparatus is controlled by the main control unit 240.

[0019] (Preparation process) First, multiple wafers 200 are loaded (wafer charged) into the boat 217.

[0020] (Boat Loading Process) Next, as shown in Figure 1, the boat 217 holding multiple wafers 200 is lifted by the boat elevator 115 and loaded into the processing chamber 201. In this state, the seal cap 219 seals the lower end of the reaction tube 204 via the base 257 and O-ring 220. At this time, the heater 206 is controlled by the temperature control unit 238 to heat the processing chamber 201 to the desired temperature. The processing chamber 201 is also evacuated by the exhaust device 246 to the desired pressure. At this time, the pressure in the processing chamber 201 is measured by the pressure sensor 245, and the pressure regulator 242 is feedback controlled based on this measured pressure.

[0021] (Heating Process) The processing chamber 201 is then heated to the processing temperature. At this time, the amount of power supplied to the heater 206 is feedback controlled based on the temperature information detected by the first temperature sensor 263 and the second temperature sensor 264 so that the processing chamber 201 has a desired temperature distribution. The control of the heater 206 based on the temperature information detected by the first temperature sensor 263 and the second temperature sensor 264 will be described in detail later. Subsequently, the wafer 200 is rotated by the rotating mechanism 254, which rotates the insulating cylinder 218 and the boat 217.

[0022] (Film Forming Process) After the temperature recovery process described later, once the processing chamber 201 reaches the processing temperature, the gas supplied from the processing gas supply source and the carrier gas supply source, and controlled by the MFC 241 to a desired flow rate, is introduced into the processing chamber 201 from multiple gas inlets 233a. The introduced gas flows down the processing chamber 201, passes through the exhaust port 231a, and is exhausted from the gas exhaust section 231. As the gas passes through the processing chamber 201, it comes into contact with the surface of the wafer 200, and processing is performed on the wafer 200.

[0023] (Cooling-down process) Once the pre-set processing time has elapsed, the processing chamber 201 is cooled down to the standby temperature. At this time, inert gas is supplied from the inert gas supply source, the processing chamber 201 is replaced with inert gas, and the pressure in the processing chamber 201 is returned to atmospheric pressure.

[0024] (Boat unloading process) Subsequently, the seal cap 219 is lowered by the boat elevator 115, opening the lower end of the reaction tube 204, and the processed wafers 200, while still held in the boat 217, are discharged from the lower end of the reaction tube 204 to the outside of the reaction tube 204. After that, the processed wafers 200 are removed from the boat 217 (wafer discharge).

[0025] Next, the control of the heater 206 by the temperature control unit 238 in this embodiment will be described in detail. The temperature control unit 238 in this embodiment can be suitably applied, for example, from the boat loading process to the film deposition process as described above. Alternatively, it may be applied from the boat loading process to the cooling process.

[0026] Figure 2 is a schematic diagram showing an example of a configuration in which the temperature control unit 238 controls the temperature of the heater 206 using the first temperature sensor 263 and the second temperature sensor 264.

[0027] In the example shown in Figure 2, the heater 206 is divided vertically into five sections, and these sections are designated as zone a, zone b, zone c, zone d, and zone e from top to bottom.

[0028] The first temperature sensor 263 detects the temperature between the reaction tube 204 and the heat-sensing tube 205. The first temperature sensor 263 is equipped with cascade thermocouples 263a, 263b, 263c, 263d, and 263e, which correspond to each zone.

[0029] The second temperature sensor 264 detects the temperature between the heat equalization tube 205 and the heater 206. The second temperature sensor 264 is equipped with heater thermocouples 264a, 264b, 264c, 264d, and 264e, which correspond to each zone.

[0030] In other words, based on the temperature information detected by thermocouples 263a to 263e and thermocouples 264a to 264e, the temperature control unit 238 adjusts the amount of power supplied to each zone of the heater 206, and is configured to control the temperature of the processing chamber 201 at the desired timing so that it reaches the processing temperature set by the higher-level controller 36.

[0031] In the following explanation, the temperature detected by the second temperature sensor 264 (thermocouples 264a to 264e) will be referred to as the heater temperature, and the temperature detected by the first temperature sensor 263 (thermocouples 263a to 263e) will be referred to as the furnace temperature.

[0032] Figure 3 is a block diagram showing the control configuration of the temperature control unit 238.

[0033] As shown in Figure 3, 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, and these components are connected to each other via a control bus 714. The memory or storage device connected to the control bus 714 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, a parameter storage area 856, and the like.

[0034] The temperature history storage area 850 stores the history of heater temperature data (heater temperature information), which is the temperature of the heater detected by the second temperature sensor 264 via the temperature input circuit 722, for a certain period of time. In addition, the temperature history of furnace temperature data (furnace temperature information), which is the temperature of the processing chamber 201 detected by the first temperature sensor 263 via the temperature input circuit 722, for a certain period of time.

[0035] The power supply value history storage area 852 stores the history (power supply value information) of the power supply value (0 to 100%) to the heater 206 for a certain period of time.

[0036] The prediction model storage area 854 stores a prediction model for each temperature zone that predicts the temperature of at least one of the heater temperature and furnace temperature data. Specifically, it stores coefficients related to the prediction model, the coefficient error correlation matrix (described later), the reference temperature, and the steady-state power value. The coefficients related to the prediction model, the coefficient error correlation matrix, the reference temperature, and the steady-state power value are stored separately for the heater temperature and furnace temperature of each zone. In addition, prediction models for the heater temperature and furnace temperature of all zones are stored as a set, with multiple sets corresponding to each temperature zone. This configuration allows for support of multiple temperature zones.

[0037] Here, the reference temperature is the temperature at which the heater temperature and furnace temperature are in a steady state (hereinafter also referred to as the processing temperature). The steady-state power value is the reference value of the prediction model, and is the power supply value for each zone when the heater temperature and furnace temperature are in a steady state at the reference temperature.

[0038] For example, the prediction model storage area 854 stores data related to the prediction model in a table format, as shown in Figure 4 or Figure 5.

[0039] Figure 4A shows the baseline values ​​for the heater temperature prediction model in zone a, and the power supply amount for each zone when the heater temperature in zone a is steady at the baseline temperature, with the baseline temperature set to 101°C. Figure 4B shows the baseline values ​​for the heater temperature prediction model in zone b, and the power supply amount for each zone when the heater temperature in zone b is steady at the baseline temperature, with the baseline temperature set to 111°C. Similar tables are created and stored for zones c through e.

[0040] Figure 4C shows the baseline values ​​for the prediction model of the furnace temperature in zone a, and shows the power supply amount for each zone when the furnace temperature in zone a is steady at the baseline temperature, with the baseline temperature set to 202°C. Figure 4D shows the baseline values ​​for the prediction model of the furnace temperature in zone b, and shows the power supply amount for each zone when the furnace temperature in zone b is steady at the baseline temperature, with the baseline temperature set to 212°C. Similar tables are created and stored for zones c through e.

[0041] Figure 5 shows that, for example, if the power supply to zone a is set to 10%, zone b to 20%, zone c to 30%, zone d to 40%, and zone e to 50%, and this state is maintained, and a steady state is reached after a sufficient amount of time has elapsed, the heater temperature in zone a will be 100°C and the furnace temperature will be 200°C, the heater temperature in zone b to be 110°C and the furnace temperature to be 210°C, the heater temperature in zone c to be 120°C and the furnace temperature to be 220°C, the heater temperature in zone d to be 130°C and the furnace temperature to be 230°C, the heater temperature in zone e to be 140°C and the furnace temperature to be 240°C. In this case, it is necessary to match the power supply values ​​in the steady state, but the memory area can be reduced compared to the case shown in Figure 4.

[0042] The parameter storage area 856 stores various parameters necessary to implement the prediction model.

[0043] The program storage area 726 stores a temperature control program that selects a prediction model for a predetermined temperature range, inputs temperature data, and controls the system to optimize the predicted temperature.

[0044] The CPU 712 executes predetermined processing based on a temperature control program stored in a program storage area 726 located in memory or a storage device. The CPU 712 can communicate with the higher-level controller 36 via a communication IF 716 to obtain the target temperature. The CPU 712 can also detect the furnace temperature and heater temperature, and output control signals to the power supply unit 718 via a temperature input circuit 722 to control and supply power to each zone a to e of the heater 206.

[0045] In other words, the temperature control unit 238 controls the heater 206 by obtaining 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 executing a temperature control program using a prediction model stored in the prediction model storage area 854. In this embodiment, an example is described in which the temperature control unit 238 executes a temperature control program that includes at least the following steps: a step to obtain temperature data of at least one of the heater temperature (the temperature of the heater 206) and the furnace temperature (the temperature of the processing chamber 201), and a power supply value to the heater 206; a step to obtain a prediction model from the prediction model storage area 854 that predicts a reference temperature for the temperature data and a predicted temperature for the temperature data; a step to calculate a power supply value using the prediction model so that the difference between the reference temperature and the predicted temperature is minimized; and a step to output the power supply value and control the heating of the heater 206. Furthermore, in this embodiment, the system is configured to include a step to create a characteristic equation using the prediction model and a step to calculate the solution to the characteristic equation.

[0046] The display / input device 720 can display and input various parameters stored in the parameter storage area 856.

[0047] [Prediction Model] Next, we will explain the prediction model stored in the prediction model memory area 854 described above. Here, the prediction model is a mathematical formula used to calculate the predicted temperature, and the following formula 1 is used.

[0048] Here, Δy(t) is the deviation of the predicted temperature at time t from the reference temperature. Also, y(t-1) and y(t-2) are the deviations of the temperature from the reference temperature one and two measurements ago, respectively. Also, p a (t-1), p a (t-2),...,p a (t-n) is the deviation of the power supply value of zone a from the steady-state power value one cycle ago, two cycles ago, ..., n cycles ago, p b (t-1), p b (t-2),...,p b(t - n) is the deviation from the steady power value of the power supply value of zone b one time ago, two times ago, ..., n times ago, p c (t - 1), p c (t - 2), ..., p c (t - n) is the deviation from the steady power value of the power supply value of zone c one time ago, two times ago, ..., n times ago, p d (t - 1), p d (t - 2), ..., p d (t - n) is the deviation from the steady power value of the power supply value of zone d one time ago, two times ago, ..., n times ago, p e (t - 1), p e (t - 2), ..., p e(t - n) is the deviation from the steady power value of the power supply value of zone e one time ago, two times ago, ..., n times ago.

[0049] a1, a2, ma1, ..., ma n , mb1, ..., mb n , mc1, ..., mc n , md1, ..., md n , me1, ..., me n are the respective coefficients. b ｉ is the constant term. The n value is a value preset in the parameter storage area 856.

[0050] Here, since Δy(t) is the deviation from the reference temperature of the predicted temperature at time t, the final predicted temperature is (Δy(t) + reference temperature). However, hereinafter, for simplicity, Δy(t) itself may be referred to as the predicted temperature.

[0051] The prediction model is stored for each zone for each of the heater temperature and the furnace temperature and can be used for control calculations. Specifically, for example, a prediction model for the predicted temperature of the furnace temperature in zone a, a prediction model for the predicted temperature of the heater temperature in zone e, etc. are stored. Note that the temperature shown in Equation 1 described above includes both the case of the heater temperature and the case of the furnace temperature.

[0052] The reference temperature and steady-state power value are acquired in the automatic thermal characteristics acquisition procedure described later, prior to creating the prediction model. The constant term bi is an adjustment term in case the previously acquired reference temperature and steady-state power value deviate from the actual values. If the previously acquired reference temperature and steady-state power value remain constant over time, the constant term bi = 0 is expected in the prediction model shown in Equation 1, which is obtained after the automatic thermal characteristics acquisition procedure. However, because the reference temperature and steady-state power value change moment by moment due to changes in the surrounding environment, power fluctuations, thermocouple noise, etc., they are included in the prediction model (Equation 1).

[0053] Furthermore, the reference temperature and steady-state power values ​​are expected to differ depending on the target temperature range, and are also expected to be nonlinear. If the reference temperature and steady-state power values ​​are inaccurate, the accuracy of the predicted temperature will decrease, affecting the control performance. Therefore, it is desirable to obtain the reference temperature and steady-state power values ​​near the predetermined processing temperature mentioned above in the oxidation and diffusion treatment described above.

[0054] According to Equation 1, if the temperature is the reference temperature, the power supply is the steady-state power value, and this condition continues, then y(t-1) and y(t-2) are zero, p a (t-1),...,p a (tn),...,p e (t-1),...p e (t-n) also becomes zero, and as a result, Δy(t) = b ｉ Therefore, the predicted temperature = bi + reference temperature. If the reference temperature and steady-state power value remain constant, then b ｉ If we obtain = 0, then the predicted temperature equals the reference temperature. In other words, it is shown that the prediction model in Equation 1 is valid in the steady state at the reference temperature.

[0055] Furthermore, according to Equation 1 described above, if we consider a predictive model for the furnace temperature in zone a, for example, it shows that, depending on each coefficient, not only the power supply to zone a, but also the power supply to zones b, c, etc., affects the furnace temperature in zone a. This makes it possible to represent the mutual thermal interference between zones, depending on each coefficient.

[0056] Furthermore, the prediction model in Equation 1 described above predicts the surrounding temperature for a given set of reference temperatures. Since the temperature rise and fall characteristics are expected to differ depending on the target temperature range, the prediction model storage area 854 can hold prediction models for multiple temperature ranges, and one of them can be selected.

[0057] Furthermore, regarding the heater temperature prediction model, Equation 2 below may be used as a substitute to simplify the calculations.

[0058] Here, Δy h (t) is the deviation of the predicted heater temperature at time t from the reference temperature. Also, y h (t-1), y h (t-2) is the deviation of the heater temperature from the reference temperature in the previous two cycles, p(t-1), p(t-2), ..., p(t-n) are the deviations of the power supply value of the corresponding zone from the steady power value in the previous two cycles, ..., n cycles, a1, a2, m1, m2, ..., m n These are the respective coefficients. ｉ This is a constant term. The n value is a value that is pre-set in the parameter storage area 856.

[0059] In other words, in Equation 2 described above, only the power supply value from the corresponding zone acts on the predicted heater temperature. Furthermore, thermal interference from zones other than the corresponding zone is not considered. For example, when calculating the predicted heater temperature of zone a, only the power supply value of zone a is used. This is because, as shown in Figure 2, the thermocouple 264a of the second temperature sensor 264 is installed near the heater 206, so it is assumed that there is no thermal influence from the heaters 206 of the other divided zones, or that it is negligibly small.

[0060] Furthermore, in Equation 2, the amount of calculation required for sum-of-products calculations is reduced compared to Equation 1, resulting in faster calculation of the predicted temperature. In addition, the number of coefficients in the prediction model that need to be determined in the automatic acquisition procedure for thermal properties, described later, is reduced, which has the advantage of speeding up the process.

[0061] Figure 6 is a control block diagram of the internal temperature control unit 238 shown in Figure 3.

[0062] As shown in Figure 6, the upper-level controller 36, the temperature control unit 238, and the heater 206 are connected, and the target temperature from the upper-level controller 36 is input to input terminal S. The furnace temperature from the first temperature sensor 263 is input to input terminal F. The heater temperature from the second temperature sensor 264 is input to input terminal H.

[0063] The target temperature and input terminal S exist in the same number as the thermocouples 263a to 263e of the first temperature sensor 263, but in Figure 6, only one is shown because they have the same configuration. Similarly, the input terminal F exists in the same number as the thermocouples 263a to 263e of the first temperature sensor 263, but in Figure 6, only one is shown because they have the same configuration. Similarly, the input terminal H exists in the same number as the thermocouples 264a to 264e of the second temperature sensor 264, but in Figure 6, only one is shown because they have the same configuration.

[0064] The internal structure of the temperature control unit 238 consists of a temperature history storage unit 800, a power supply value history storage unit 802, an individual characteristic creation unit 804, a target temperature sequence calculation unit 806, an integrated characteristic creation unit 808, a constrained optimization calculation unit 810, a limiter 812, and a power supply unit 718.

[0065] The temperature history storage unit 800 receives the furnace temperature from the first temperature sensor 263 via the input terminal F and stores it in the temperature history storage area 850 for a certain period of time. The temperature history storage unit 800 writes data to the temperature history storage area 850 sequentially at predetermined intervals, starting from the first acquired furnace temperature. After the temperature history storage area 850 is filled with data, the oldest data is discarded and new data is written to its place. In this way, data on the furnace temperature from the past for a certain period of time from the present is always stored.

[0066] To ensure a consistent understanding of time, the furnace temperature written in the current t process, as shown in the control algorithm, is treated as y(t-1) (= the temperature from the previous cycle) as shown in Equation 1. The acquired furnace temperature is calculated from the average of the electromotive forces of thermocouples 263a to 263e up to the time of writing.

[0067] The power supply value history storage unit 802 receives the power supply value output from the output terminal P and stores that data in the power supply value history storage area 852 for a certain period of time. The power supply value history storage unit 802 writes the power supply value history storage area 852 sequentially at predetermined intervals, starting from the first power supply value acquired. After the power supply value history storage area is filled with data, the oldest data is discarded and new data is written to its place. In this way, data of power supply values ​​from the past for a certain period of time from the present is always stored.

[0068] To unify the understanding of time, the power supply value written in the current process t, as shown in the control algorithm, is given by p, as shown in Equation 1. a (t-1), p b (t-1), p c (t-1), p d (t-1), p e This is treated as (t-1) (= the power supply value from the previous cycle). This value represents the amount of power that was calculated in the previous process and continues to be supplied up to the current time.

[0069] The individual characteristic creation unit 804 obtains a prediction model of the furnace temperature in the zone from the prediction model storage area 854, obtains current and past data of a predetermined furnace temperature from the temperature history storage area 850, obtains current and past data of a predetermined power supply value from the power supply value history storage area 852, and creates the individual input response characteristic matrix S described below by Equations 3 and 4. sr and individual zero response characteristic vector S zr The individual input response characteristic matrix S is calculated. sr and individual zero response characteristic vector S zr This calculates only the number of internal reactor temperatures to be controlled (i.e., the number of zone divisions).

[0070] The above equation 1 can be expressed using a state-space model as shown in equation 3 below.

[0071] Here, matrices A, B, and C are as follows. For simplicity of notation, we will use the deviations from the steady-state power values ​​of the power supply values ​​in zones a to c up to four cycles ago (n=4). In the following examples, for simplicity of notation, we will use zones a to c up to four cycles ago, but we are not limited to this.

[0072] Furthermore, the vectors x(t), u(t), and output y(t) are as follows. To continue simplifying the notation, we will use the deviations from the steady-state power values ​​of the power supply values ​​in zones a to c from the previous four times (n=4).

[0073] In Equation 3, if we input the power supply value u(t) at time t and continue to input u(t) thereafter, the predicted temperature from t+1 onwards will be as shown in Equation 4.

[0074] Here, in equation 4, S zr This is the individual zero response characteristic vector, S sr Δy(t) is the individual input response characteristic matrix, and Δy(t) is the predicted temperature vector.

[0075] Each row represents the number of calculations for the predicted temperature, and the number of calculations performed depends on the control cycle and the processing performance of the CPU 712, up to a certain limit.

[0076] Individual zero-response characteristic vector S zr This shows the amount of change that is influenced by past furnace temperatures and past power supply values. Also, the individual input response characteristic matrix S sr This shows the amount of change that is affected by the current furnace temperature and power supply value.

[0077] The following is the individual input response characteristic matrix S. sr Individual zero-response characteristic vector S zr And, when the predicted temperature vector Δy(t) is distinguished by corresponding zone, the individual input response characteristic matrix corresponding to zone a is S sr-a The individual zero response characteristic vector corresponding to zone b is S zr-b The predicted temperature vector corresponding to zone e is Δy e (t) is used as a notation.

[0078] The target temperature sequence calculation unit 806 receives the target temperature from the upper-level controller 36 via the input terminal S and generates a target temperature sequence vector S representing the target values ​​of future temperature changes in vector form. tg The target temperature obtained from the input terminal S is given a final target temperature and a ramp rate, in addition to the moment-by-moment target temperature set for each future time point. The ramp rate is the rate of change when the temperature changes from the current target temperature to the final target temperature, and indicates the amount of temperature change per unit time. For example, if the setting is 1°C / min, it indicates a change of 1°C per minute. That is, the target temperature column vector S tg This is calculated by inputting the target temperature, final target temperature, and ramp rate. Target temperature column vector S tg This calculates only the number of furnace temperatures to be controlled (i.e., the number of zone divisions). Target temperature column vector S tg For the purposes of the following explanation, it will be expressed as shown in equation 5 below.

[0079] The time and row number in Equation 5 correspond to the time and row number in Equation 4. Below, the target temperature column vector S tg When distinguishing by corresponding zone, if it corresponds to zone a, then S tg-a , if it corresponds to zone e, S tg-e This is how it is written.

[0080] Here, the predicted temperature at the current time (current predicted temperature) can be calculated from past temperature data by moving the time forward one step from time t. Furthermore, at the current time, the measured temperature is clearly defined. The difference between this previous predicted temperature (current predicted temperature) and the measured temperature is defined as the prediction error. The prediction error is calculated by comparing the temperature at the current time (measured temperature) with the aforementioned individual zero-response characteristic vector S. zrIn relation to the power supply values ​​to be output in the future, this indicates the amount of deviation between the predicted temperature already determined by past furnace temperatures and power supply values. Here, the difference between the current predicted temperature and the current actual temperature indicates the accuracy of the predicted temperature at the previous time t. If the difference is almost negligible, it can be judged that the previous predicted temperature was correct; conversely, if the difference is large, it can be judged that the previous predicted temperature was different from reality.

[0081] From the temperature history storage unit 800 to the target temperature sequence calculation unit 806, the heater 206 is divided, so there are as many input terminals S and F as there are divisions, but in Figure 6, only one of each is shown for simplicity.

[0082] The integrated characteristic creation unit 808 generates individual input response characteristic matrices S obtained by the individual characteristic creation unit 804, which has a number of zone divisions. sr and individual zero response characteristic vector S zr The input is used, and the target temperature sequence vector S obtained by the target temperature sequence calculation unit 806, which has a number of zone divisions, is used. tg Enter the values ​​to create the integrated characteristic equation.

[0083] First, the individual input response characteristic matrix S sr The following is transformed: Individual input response characteristic matrix S sr This shows the change in predicted temperature when u(t) is input at time t and u(t) is continued to be input thereafter. If u(t) is not held and different values ​​u(t) to u(t+Np-1) are input at all control timings, the second term on the right side of equation 4 becomes as follows. Here, Np is the row number in equation 4.

[0084] In well-known model predictive control, it is assumed that different values ​​u(t) to u(t+Np-1) are input at the timing of all calculation processes, and these are calculated to determine the result. However, because the calculation processing performance of the CPU 712 is insufficient, in this disclosure, the input pattern is limited to two stages, and the second term on the right side of Equation 4 is changed as follows.

[0085] Here, Ncd is 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. The input of the second stage is u(t + Ncd) and is held thereafter. The individual input response characteristic matrix S is as described above. sr By rearranging equation 4, we obtain equation 6 as shown below.

[0086] In equation 6, S dsr This is then designated as the individual input response characteristic matrix. When distinguishing by corresponding zone, the individual input response matrix corresponding to zone a is S dsr-a This is how it is written.

[0087] Next, regarding equations 6 and 5 described above, we list all the zones to be controlled.

[0088] As described above, the integrated characteristic creation unit 808 generates the integrated input response characteristic matrix U shown in Equations 7 and 8. dsr Integrated zero response characteristic vector U zr Integrated target temperature vector U tg Calculate and output the result.

[0089] Next, the constrained optimization calculation unit 810 calculates the integrated input response characteristic matrix U obtained by the integrated characteristic creation unit 808. dsr Integrated zero response characteristic vector U zr Integrated target temperature vector U tg The optimal power supply value for the current situation is calculated by inputting the upper and lower limit values ​​for each zone used in the limiter 812 described later, and by using the effective constraint method, which seeks the solution that minimizes the given constraints. The effective constraint method and the operation of the constrained optimization calculation unit 810 to which it is applied will be described later.

[0090] The limiter 812 then restricts the calculation result to the range that the heater 206 can output, and sets this as the power supply value to the heater 206. Here, the output of the limiter 812 is set as a percentage of the maximum output of the heater 206, for example, to 0-100%. The limit value of the limiter 812 may change depending on the heating temperature of the heater 206. Therefore, the heater temperature can be obtained from the input terminal H, and a limit value can be derived from a temperature limit table (not shown) corresponding to the heater temperature, and the limit can be set to that value. The upper and lower limits indicating the output range are then made available for use by other processing units.

[0091] The power supply unit 718 then controls the amount of power supplied to the heater 206 via the output terminal P so that it corresponds to a power supply value between 0 and 100%.

[0092] Note that the limiter 812 and power supply unit 718 exist in quantities corresponding to the number of divisions of the heater, along with the output terminal P, but in Figure 6, only one of each is shown for simplicity.

[0093] [First Effective Constraint Method] The first effective constraint method used in this disclosure is described below. The effective constraint method finds the solution vector x that maximizes the evaluation function f(x) given by the following equation 9, under the constraints of the following equation 10.

[0094] In equations 9 and 10, c, Q, b, and A are given constant matrices or vectors. The symbol T represents the transpose. In this case, the effective constraint method can find the solution vector x by performing the flow shown in Figure 7.

[0095] In S201, the solution x is in the range where the equality in equation 10 is not valid. k Select A. Then, select the set of rows in equation 10 where the equality sign is valid. e , b e Let's assume that in S201, A e , b e Both are empty sets. Also, the set of rows in equation 10 where the equality sign is not valid is A. d , b d Let's assume that in S201, A d = A, b d= b.

[0096] In S203, solve the following system of simultaneous equations, and let the solutions be x and λ. x = x k If so, proceed to S205. If x ≠ x k If so, proceed to S207.

[0097] In S205, determine whether all elements of λ are 0 or more. If they are 0 or more, proceed to S213. If not all elements of λ are 0 or more, proceed to S211.

[0098] In S207, obtain α according to the following Equation 11. In Equation 10, b i , a i are respectively extracted from one row of A d , b d respectively. If α = 1, proceed to S205. If α < 1, proceed to S209.

[0099] In S209, the constraints {b i , a i} used when obtaining α (< 1) according to Equation 11 are deleted from A d , b d and added to A e , b e , and then proceed to S203.

[0100] In S211, select the element of λ that is the minimum and negative, and delete the corresponding one {b i , a i} among the constraints included in Ae and be from A e , b e and add it to A d , b d , and then proceed to S203.

[0101] In S213, end with the solution x obtained in S203 as the optimal solution.

[0102] The active constraint method shown in FIG. 7 can obtain a solution that satisfies Equation 10 and maximizes Equation 9 by searching for a combination of rows for which the equal sign becomes effective among the rows of Equation 10 using the Lagrange multiplier λ.

[0103] [Application of the Effective Constraint Method in the Constrained Optimization Calculation Unit 810] Next, the method for applying the effective constraint method in the constrained optimization calculation unit 810 in this embodiment will be described.

[0104] In the integrated characteristics creation unit 808, the predicted temperature sequence (predicted temperature vector) of the furnace temperature was obtained using equation 7, and the target temperature sequence (integrated target temperature vector) was obtained using equation 8. Therefore, the constrained optimization calculation unit 810 adopts the square of the error between the target temperature sequence and the predicted temperature sequence as the evaluation function. The evaluation function V(u(t)) is given by the following equation 12.

[0105] Comparing the contents of the parentheses outside the second term of Equation 12 with Equation 9, we can see that c and Q in Equation 9 can be replaced with the following equations, respectively.

[0106] This allows us to obtain a solution that maximizes the expression inside the outer parentheses of the second term in Equation 12 using the effective constraint method described above. Therefore, we can find a solution that minimizes the evaluation function V(u(t)), and thus determine the power supply value that minimizes the square of the error between the target temperature sequence and the predicted temperature sequence.

[0107] Next, regarding equation 10 concerning the constraints, to simplify the notation, we will use zones a to c from the previous four sections as an example, and as shown in the following equation 13, the power supply value P for each zone a , P b , P c If upper and lower limits are given to each of the arrows on the left, then we can apply them to equation 10 by setting up an inequality as shown on the right of the arrow. In the following equation 13, LL ａ , UL ａ These are the upper and lower limits of the power supply value for zone a, and LL ｂ , UL ｂ , LL ｃ , UL ｃ Similarly, these are the upper and lower limits of the power supply values ​​for zone b and zone c, respectively. For example, LL ａ = 0%, UL ａ It will be set to something like =80%.

[0108] [Second Effectiveness Constraint Method]

[0109] Next, a second effective constraint method available in this disclosure will be described. In the effective constraint method shown in Figure 7 above, if the processing power of the CPU 712 was insufficient, the calculation may not be completed within the predetermined control cycle. Therefore, instead of the flow in Figure 7, the solution vector x can be obtained using the flow in Figure 8.

[0110] The difference from the first effective constraint method in Figure 7 is that S215 is added immediately after the start, S201 is changed to S217, the process proceeds from S209 and S211 to the added S219, and the process proceeds to either S203 or S213 based on the determination in S219. Below, only the difference from the first effective constraint method will be explained.

[0111] In S215, the loop count is initialized.

[0112] Then, in S217, the solution x in the range where the equality in equation 10 is not valid is obtained. k Select this. In case the optimization calculation terminates prematurely in S219, described later, the selected solution is specifically set as the lower limit of the range where the equality in equation 10 is not valid. For example, with respect to the constraint on the power supply value Pa in zone a, 0 ≤ P a If (t) ≤ 100, the selected solution is P a Let (t) = 0.1, for example. By making this selection, the lower bound constraint takes precedence over the constraints added in S209, so even if the optimization calculation is terminated prematurely, a safe calculation result can be obtained.

[0113] In S219, the number of loop iterations is counted up. If it is within the predetermined number of iterations, the program proceeds to S203. If it exceeds the predetermined number of iterations, the program proceeds to S213 and terminates, considering the solution x obtained in the previous S203 as the optimal solution.

[0114] By using a flow chart like the one shown in Figure 8, the calculation of the optimal solution can be completed with the minimum necessary processing, allowing the calculation to be completed within the predetermined control cycle.

[0115] <Modified Version> Figure 9 is an internal control block diagram of a temperature control unit 238 showing a modified version according to one embodiment of the present disclosure. When temperature control was actually performed using the control block diagram shown in Figure 6, the steady-state error sometimes did not asymptotically approach zero. Therefore, the control block in Figure 9 was made to enable control. In the modified version, a subtraction unit 814, an integration unit 816, and a prediction error calculation unit 818 are added to the control block diagram shown in Figure 6, and an integrated characteristic creation unit 820 is used instead of the integrated characteristic creation unit 808. In the following, only the parts that differ from the control block shown in Figure 6 described above will be explained below, and detailed explanations of the parts that are the same will be omitted.

[0116] There are as many subtraction units 814 as there are zone divisions. The target temperature, which changes moment by moment, is input from input terminal S, and the furnace temperature is input from input terminal F, and the subtraction unit 814 calculates the difference between them.

[0117] The integration unit 816 exists in a number equal to the number of zone divisions, and integrates the deviation obtained by the subtraction unit 814. The calculation method is shown in the following equation 14.

[0118] Here, dev(t) is the deviation obtained by the subtraction unit 814. The initial value of the integral is set to zero. Also, T ｉ This is an integration constant, obtained from parameter storage area 856. In particular, to prevent the integration of the deviation from negatively affecting control performance, integration is not performed when the deviation is large. It also has a so-called ARW (Anti-Reset Wind-Up) function that does not perform integration when the previous power supply value for the corresponding zone is at the upper or lower limit. The left side is set to (t-1) because the furnace temperature obtained in the current process is treated as y(t-1) (= the temperature from the previous cycle), and this is adjusted accordingly. Also, the integral value of the deviation S yi When distinguishing by corresponding zone, if it corresponds to zone a, then S yi-a , if it corresponds to zone e, S yi-e This is how it is written.

[0119] The prediction error calculation unit 818 obtains a prediction model from the prediction model storage area 854, obtains current and past data of a predetermined furnace temperature from the temperature history storage area 850, obtains current and past data of a predetermined power supply value from the power supply value history storage area 852, and calculates the prediction error. The prediction error is calculated for each of the number of furnace temperatures to be controlled (= number of zone divisions).

[0120] First, we calculate the error between the furnace temperature obtained this time and the predicted temperature for that temperature using Equation 1 mentioned above. Next, we apply a low-pass filter to the calculated error, as shown in Equation 15 below.

[0121] Here, Δy(t-1) is the predicted temperature for the previous temperature obtained this time, and can be obtained from Equation 1. Also, F e is the filter coefficient, which is obtained from the parameter storage area 856. The left side is set to (t-1) because the furnace temperature obtained in this process will be treated as y(t-1) (= the temperature from the previous step), and this has been adjusted accordingly. Also, the prediction error S pe When distinguishing by corresponding zone, if it corresponds to zone a, then S pe-a , if it corresponds to zone e, S pe-e This is how it is written.

[0122] From the subtraction unit 814 to the prediction error calculation unit 818, there are as many input terminals S and F as there are heater divisions, similar to the temperature history storage unit 800 to the target temperature sequence calculation unit 806, but in Figure 9, only one of each is shown for simplicity.

[0123] The integrated characteristic creation unit 820 replaces the integrated characteristic creation unit 808 shown in Figure 6. The integrated characteristic creation unit 820 generates individual input response characteristic matrices S obtained by the individual characteristic creation unit 804, which has a number of zone divisions. sr and individual zero response characteristic vector S zr The input is used, and the target temperature sequence vector S obtained by the target temperature sequence calculation unit 806, which has a number of zone divisions, is used. tgThe integrated characteristic equation is created by inputting the integral value of the deviation obtained by the integration unit 816 with a number of zone divisions, and the prediction error obtained by the prediction error calculation unit 818 with a number of zone divisions. The added integral value of the deviation and prediction error are applied as follows: that is, equations 7 and 8 are replaced as shown in equation 17 below.

[0124] Here, for example, vector S zr-a ni Scala S pe-a The part where it is added indicates that a scalar is added to all elements of the vector.

[0125] As described above, the integrated characteristic creation unit 820 generates the integrated input response characteristic matrix U shown in equations 16 and 17. dsr Integrated zero response characteristic vector U zr Integrated target temperature vector U tg Calculate and output the result.

[0126] According to the control method shown in Figure 9, prediction errors due to various short-term factors such as noise can be eliminated during control calculations by correcting the predicted temperature sequence, thereby reducing the steady-state error. Furthermore, prediction errors due to long-term factors such as environmental fluctuations and invariant factors such as deviations in the prediction model can be eliminated by correcting the target temperature with the integral of the deviation, thereby eliminating the steady-state error.

[0127] [Automatic acquisition procedure for thermal characteristics] Next, the automatic acquisition procedure for thermal characteristics performed by the temperature control unit 238 will be explained using Figure 12. The automatic acquisition procedure for thermal characteristics shown below creates a prediction model necessary for control by the temperature control unit 238 and stores it in the prediction model storage area 854.

[0128] First, to initiate the automatic acquisition of thermal characteristics, the higher-level controller 36 provides a reference temperature for each furnace temperature. The temperature control unit 238 then controls the furnace temperature using PID-based feedback control in S300 and S302.

[0129] In S300, the temperature control unit 238 controls the furnace temperature and continues processing until the furnace temperature rises to or falls to near the reference temperature. At this time, the parameters used for control obtained from the parameter storage area 856 (for example, PID parameters not shown) need to be asymptotically stable, but do not necessarily need to be optimal.

[0130] In S302, the temperature control unit 238 controls the furnace temperature and continues this process until the furnace temperature is controlled to a reference temperature and a steady state is reached. At this time, the parameters used for control (e.g., PID parameters not shown) obtained from the parameter storage area 856 need to be asymptotically stable, but do not necessarily need to be optimal. When it is determined that a steady state has been reached, the power supply value at that time, or a constant time average of the power supply value, is written to the prediction model storage area 854 as the steady power value. Also, when it is determined that a steady state has been reached, the heater temperature at that time, or a constant time average of the heater temperature, is written to the prediction model storage area 854 as the reference temperature for the heater temperature. In addition, the reference temperature for the furnace temperature is written to the prediction model storage area 854.

[0131] In S304, for a predetermined time from the start time of this step, a random value is output to the heater 206 as a power supply value via the power supply unit 718. At the same time, the current and past furnace temperature and heater temperature 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 prediction model for the furnace temperature is updated and stored using the obtained current and past furnace temperatures and current and past power supply values. Then, the prediction model for the heater temperature is updated and stored using the obtained current and past heater temperatures and current and past power supply values.

[0132] Here, the random values ​​are four discrete values ​​centered around the steady-state power values ​​stored in the prediction model memory area 854, and are selected randomly. Then, the power supply value of one zone is changed at a predetermined time interval (for example, 1 minute). The zone to be changed at a given time is selected randomly. The updating of the prediction model will be described later.

[0133] In S306, for a predetermined time from the start time of this step, the steady-state power value is output to the heater 206 as the power supply value via the power supply unit 718. At the same time, the current and past furnace temperature and heater temperature 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 prediction model for the furnace temperature is updated and stored using the obtained current and past furnace temperatures and current and past power supply values. Then, the prediction model for the heater temperature is updated and stored using the obtained current and past heater temperatures and current and past power supply values.

[0134] In S308, the same process as in S304 is performed, and in addition, the updated prediction model is evaluated. If the evaluation determines that the prediction model is valid, the process proceeds to S310. The evaluation of the prediction model will be described later.

[0135] In S310, the prediction model acquired in S308 is used to control the target furnace temperature using the temperature control method shown in Figure 9, and this process is carried out until the furnace temperature is controlled to the reference temperature and a steady state is reached. When it is determined that a steady state has been reached, the steady power value, the reference temperature of the heater, and the reference temperature are updated in the same manner as in S302.

[0136] In S312, the same process as in S308 is performed. If the evaluation results indicate that the prediction model is valid, the automatic acquisition procedure for thermal characteristics is terminated.

[0137] Figure 13 illustrates the internal processing block diagram of the temperature control unit 238 in steps S304, S308, and S312 of the automatic thermal characteristics acquisition procedure.

[0138] In Figure 13, the temperature control unit 238 includes a furnace temperature prediction model update unit 834, a heater temperature prediction model update unit 836, a prediction model evaluation unit 838, a random power output unit 840, and the like. The reference temperature, steady-state power values, etc., related to the prediction model have already been acquired and are stored in the prediction model storage area 854.

[0139] First, as described above in S304, the random power output unit 840 outputs a randomly selected value from among the four discrete values ​​centered on the steady-state power value to the limiter 708. Furthermore, although there are as many random power output units 840 as there are divisions of the heater 206, as described later, they cooperate with each other to change the power supply value of one randomly selected zone at a preset time interval (for example, 1 minute), as mentioned above.

[0140] Next, the furnace temperature prediction model update unit 834 obtains a prediction model for the furnace temperature of the zone from the prediction model storage area 854, obtains current and past data for a predetermined furnace temperature from the temperature history storage area 850, obtains current and past data for a predetermined power supply value from the power supply value history storage area 852, calculates and updates the latest furnace temperature prediction model available at that time.

[0141] Next, the heater temperature prediction model update unit 836 obtains a prediction model for the heater temperature of the zone from the prediction model storage area 854, obtains current and past data for a predetermined heater temperature from the temperature history storage area 850, obtains current and past data for a predetermined power supply value from the power supply value history storage area 852, calculates and updates the latest heater temperature prediction model available at that time.

[0142] The furnace temperature prediction model update unit 834, the heater temperature prediction model update unit 836, and the random power output unit 840 each exist in quantities corresponding to the number of divisions of the heater 206, but in Figure 13, only one of each is shown for simplicity.

[0143] Next, the prediction model evaluation unit 838 acquires prediction models for the furnace temperature and heater temperature, which are divided into zones, at a preset evaluation interval (for example, 10 minutes), and evaluates the acquired prediction models until the next acquisition timing after the evaluation interval. Based on the evaluation results, it determines whether the prediction model is valid or invalid.

[0144] [Method for updating the prediction model] Next, the method for updating the prediction model performed in the furnace temperature prediction model update unit 834 and the heater temperature prediction model update unit 836 shown in Figure 13 in S304, S308 and S312 described above will be explained. As described below, the prediction model for furnace temperature and the prediction model for heater temperature can be updated using similar processing. The update method disclosed herein uses a method called the successive least squares method. Equation 27 below is Equation 1 expressed using matrices and vectors.

[0145] Here, time t represents the current process, and the reason why the latest data among the elements of x(t) is y(t-1) is because, as mentioned above, the time t-1 represents the temperature and power supply values ​​obtained in this process.

[0146] The coefficients θ(t) of the latest prediction model are calculated as shown in equation 28 below.

[0147] Here, y(t-1) is the temperature obtained in this test, which is the furnace temperature or heater temperature targeted by the prediction model. ρ is a parameter called the forgetting coefficient, which is obtained from the parameter storage area 856. P(t) is the coefficient error correlation matrix, for example, an identity matrix with elements from 100 to 1000 is set as the initial value.

[0148] The θ(t) obtained in Equation 28 may, depending on the input x(t), be clearly unsuitable for predicting temperature, or may cause oscillations if used for control. Therefore, if the following conditions 1 to 4 regarding model updates are met, instead of following Equations 1 and 4 of Equation 28, the coefficient error correlation matrix P(t) and the coefficient θ(t) of the prediction model are set to the same values ​​as before.

[0149] The first condition for updating the model was that the temperature targeted by the prediction model deviated from the vicinity of the reference temperature (e.g., ±50°C).

[0150] The second condition for model updating was that if even one element of the coefficient θ(t) of the prediction model fell outside a predetermined range (for example, -100 to +100).

[0151] The third condition for model updating is that among the elements of the coefficient θ(t) of the prediction model, m ａ1 (t), ..., m ａn (t), m ｂ1 (t), ...m ｂn (t), ..., m ｅn We considered the case where the sum of (t) is negative.

[0152] The fourth condition for model updating is the transfer function composed of a1(t) and a2(t) elements of the coefficient θ(t) of the prediction model.

[0153] This was assumed to be the case where it is unstable.

[0154] However, when the number of calculations in Equation 28 is small, depending on the input x(t), the first to fourth conditions for model updating may be met consecutively. In such a situation, the predictive model will never achieve the desired accuracy. Therefore, it is also possible to ignore the first to fourth conditions for model updating and update the coefficients θ(t) of the predictive model for a predetermined number of times.

[0155] If the coefficients θ(t) of the prediction model obtained by Equation 28 do not meet any of the first to fourth conditions described above, they are stored in the prediction model storage area 854 along with the coefficient error correlation matrix P(t).

[0156] The coefficients θ(t) of the prediction model are determined in S308 and S312 above if the evaluation results are valid, and are read out and used by the individual characteristic creation unit 804 shown in Figure 6, the individual characteristic creation unit 824 shown in Figure 10, the prediction error calculation unit 818 shown in Figure 9, etc.

[0157] [Method for Evaluating the Predictive Model] The method for evaluating the predictive model performed in the predictive model evaluation unit 838 shown in Figure 13, as described above in S304, etc., will be explained below.

[0158] Predictive models for furnace temperature and heater temperature are acquired at predetermined evaluation intervals (e.g., 10 minutes), and the acquired predictive models are evaluated until immediately before the next timing. The acquired predictive models are deemed valid when all of the following conditions 1 to 3 regarding the evaluation method are satisfied.

[0159] The first condition regarding the evaluation method was that all predictive models did not meet any of the first to fourth conditions regarding model updates.

[0160] The second condition regarding the evaluation method is that for all prediction models, the sum of the changes in prediction model coefficients C, calculated using the following equation 29, is applied. vg (t) was calculated at every time the prediction model was updated, and the maximum value of these calculations was set to be less than or equal to a predetermined convergence criterion.

[0161] The third condition regarding the evaluation method is that, for all prediction models, the prediction error obtained using the prediction model is calculated at the timing of all processing in the evaluation interval, and these must be less than or equal to a predetermined error threshold. Prediction error E in the evaluation method pe (t) is calculated as shown in equation 30 below.

[0162] The coefficients θ of the prediction model in Equation 30 are constants because they are obtained in the first processing of the evaluation interval and remain unchanged until the next acquisition process after the evaluation interval has elapsed. The input x(t) is obtained in the first processing of the evaluation interval,

[0163] And in the next second process...

[0164] And in the following third and subsequent processing...

[0165] In other words, at the initial processing stage to obtain the prediction model for evaluation, the current and past measured temperatures obtained from the temperature history storage area 850 are used as the past temperature data for prediction, but in subsequent processing, the predicted temperature calculated in the previous processing stage is used.

[0166] Next, an example of a substrate processing sequence performed by the substrate processing apparatus 10 will be described using Figures 10A and 10B. Here, the temperature control unit 238 is configured to control the power supplied to the current heater 206 at each step of the substrate processing sequence so that the predicted temperature sequence calculated according to a pre-held prediction model approaches the future target temperature sequence.

[0167] In step S101 (waiting step), the wafer 200 is maintained at the waiting temperature (waiting temperature) before being brought into the processing furnace 202 (or processing chamber 201). In step S101, for example, the wafer 200 may be transported to the boat 217.

[0168] Step S102 (boat loading step) is a step in which the wafer 200 is loaded into the processing furnace 202 (or processing chamber 201). For example, in this embodiment, the wafer 200 is loaded into the processing furnace 202 (or processing chamber 201) while being held in the boat 217. At this time, the temperature of the boat 217 and the wafer 200 is lower than the standby temperature T0, and as a result of loading the wafer 200 into the processing furnace 202 (or processing chamber 18), the atmosphere from outside the processing furnace 202 (room temperature) is introduced into the processing furnace 202 (or processing chamber 18), so the temperature inside the processing furnace 202 (or processing chamber 201) temporarily becomes lower than the standby temperature T0. After that, the temperature inside the furnace reaches the standby temperature T0 again after a short time due to control by the temperature control unit 238.

[0169] Step S103 (stabilization step) is a step to maintain and stabilize the furnace temperature at the standby temperature T0.

[0170] Step S104 (heating step) is a step in which the furnace temperature is raised from the standby temperature T0 to the processing temperature T1. The temperature control unit 238 controls the heater 206 so that the furnace temperature becomes a target temperature T1, which is higher than the standby temperature T0.

[0171] Step S105 (processing step) is a step in which the furnace temperature is maintained at a target temperature T1 in order to process the wafer 200 and the wafer 200 is processed. After a predetermined time has elapsed, a cooling step is performed.

[0172] Step S106 (boat unloading step) is a step in which the processed wafer 200 is removed from the processing furnace 202 (or processing chamber 201) together with the boat 20.

[0173] If there are any unprocessed wafers 200 that need to be processed, the processed wafers 200 are removed from the boat 20 and replaced with the unprocessed wafers 200, and this series of processes from steps S101 to S106 is performed one or more times.

[0174] In step S104 (heating step) shown in Figure 10B, the temperature control unit 238 controls the power supplied to the current heater 206 so that the predicted temperature sequence calculated according to a pre-held furnace temperature prediction model approaches the future target temperature sequence, thereby converging the furnace temperature to the target temperature T1 and shortening the recovery time from the heating step (step S104) to the processing step (step S105). Similarly, the above-described temperature control by the temperature control unit 238 can also be used in boat loading (step S102) and boat unloading (step S106).

[0175] At this time, the temperature control unit 238 calculates a future temperature prediction sequence based on past temperatures and a previously acquired temperature characteristic model (prediction model) assuming a constant output of steady-state power. Next, the temperature control unit 238 calculates the difference between the current predicted temperature calculated from the temperature prediction sequence and the actual temperature as the prediction error. Specifically, the temperature control unit 238 obtains the prediction model from the prediction model storage area 854, obtains current and past data of a predetermined furnace temperature from the temperature history storage area 850, obtains current and past data of a predetermined power supply value from the power supply value history storage area 852, and calculates the prediction error. Then, the temperature control unit 238 uses the calculated prediction error as the prediction deviation amount from the previous prediction and updates the future temperature prediction sequence using this prediction deviation amount. Here, the temperature prediction sequence is created at the current time (t) based on the temperature prediction sequence at a past time (t-1). Note that the control cycle of the temperature control unit 238 is t.

[0176] Figure 11 is a diagram illustrating an example of the processing of the integrated characteristic creation unit 808 (Figure 6) or the integrated characteristic creation unit 820 (Figure 9) when using the temperature control unit 238 described above. In Figure 11, the heating process (step S104) is explained, but it goes without saying that this embodiment is not limited to this process.

[0177] Figure 11A is an illustrative diagram showing how the predicted temperature sequence is calculated from past temperatures and a previously acquired temperature characteristic model, assuming a constant steady-state power output. In this case, the temperature control unit 238 calculates the individual zero-response characteristic vector S from past temperatures (t-1) and a previously acquired temperature characteristic model, assuming a constant steady-state power output. zr This calculates the current predicted temperature. This allows us to determine the current predicted temperature. Figure 11B is an illustrative diagram showing how the difference between the calculated current predicted temperature and the measured temperature is calculated as the prediction error. The temperature control unit 238 calculates the difference between the predicted temperature at the current time (t) calculated in this way and the measured temperature at the current time (t) as the prediction error. Here, the prediction error is calculated by comparing the measured temperature at the current time (t) with the individual zero response characteristic vector S zr In relation to this, it shows the amount of deviation between the predicted temperature already determined by past furnace temperatures and power supply values, regardless of the power supply values ​​to be output in the future. Figure 11C is an illustrative diagram of how the predicted temperature sequence is corrected using the prediction error, regardless of the magnitude of the deviation. Specifically, the temperature control unit 238 uses this prediction error to create an individual zero response characteristic vector S zr By correcting for this, the deviation from the previous prediction is reflected in the predicted temperature from time t onward.

[0178] Let y(t-1) be the predicted temperature at the current time, and y be the actual temperature. act Therefore, the prediction error P dev The result is as follows: P dev = y act - y(t-1) Here, for example, the predicted temperature sequence of the integrated characteristic creation units 808 and 820 is as follows.

[0179] Here, P dev (t) is expressed as follows:

[0180] Here, P devThe system corrects the prediction error by accumulating the correction amount according to the coefficient k each time time t is moved one step into the future. The prediction error is considered to be the amount of deviation from the prediction that occurs when time t has elapsed, and by correcting so that the amount of prediction error increases each time time t+1, t+2, etc., the amount of deviation from the prediction after time t can be reduced. For example, by setting the coefficient k to a number greater than or equal to 1, the amount of prediction deviation at the current time can be corrected each time time t has elapsed, and this is appropriate as a standard value. However, if the in-furnace conditions from which the prediction model was acquired, specifically pressure, gas flow rate, number of wafers 200, etc., differ significantly, the amount of correction for deviation from the prediction error can be adjusted by changing the coefficient k.

[0181] In this embodiment, the coefficient k is 1, and specifically, P dev (t) is corrected by doubling, tripling, and accumulating the predicted error amount each time time t is moved one step into the future (control cycle).

[0182] The temperature control unit 238 calculates the power supply value so that the corrected predicted temperature sequence matches the target temperature sequence provided by the higher-level controller 36. In this embodiment, the prediction error decreases with each iteration of the prediction error calculation, so that the corrected predicted temperature sequence and the target temperature sequence provided by the higher-level controller 36 can be made to match. In this embodiment, the temperature control by the temperature control unit 238 is performed using the predicted temperature sequence corrected with a coefficient k value of 1, not only in the heating step (step S104) but also in the processing step including the cooling step (step S105). However, in the cooling step, the coefficient k is -1 (minus 1). Note that during film formation, temperature control is performed with a coefficient k of 1. This is because the temperature is constant (prediction error is almost zero) during film formation, and therefore it is not affected by the value of the coefficient k.

[0183] According to this embodiment, the insufficient correction of prediction errors, particularly in the heating step (step S104), is eliminated. In this way, by appropriately selecting (setting) the value of the coefficient k, the prediction error calculated at time t+1 can be made smaller than the prediction error calculated at time t. In other words, the predicted temperature sequence derived from the prediction error can be made appropriate. This suppresses temperature fluctuations caused by continuous deviations in prediction errors. Furthermore, based on a preset target temperature or heating (cooling) step, the furnace can be maintained at an appropriate temperature, or the furnace can be made to follow a specified temperature change without overshooting.

[0184] Furthermore, because temperature fluctuations during heating are suppressed, the reproducibility of the thermal history of the wafer 200 is expected in run-to-run testing. In addition, concerns that the temperature of a part of the wafer 200, such as the edge (end) near the heat source, may become higher than expected and adversely affect the underlying film of the wafer 200 are eliminated.

[0185] Furthermore, the temperature control unit 238 according to this embodiment can suppress overshoot and reduce inter-zone deviations. In addition, even when there is a large variation in the individual temperature characteristics of the heaters, or when the assigned engineer does not have enough time, the thermal characteristics can be acquired automatically, and the optimal control method can be obtained without parameter adjustment, or by easily adjusting the parameters. As a result, the expected performance of the device can be easily obtained.

[0186] Although embodiments of the present disclosure have been specifically described above, the present disclosure is not limited to the embodiments and examples described above, and can be modified in various ways without departing from its essence. For example, in this embodiment, the coefficient is set to 1, but it is not limited to this, and may be a value smaller than 1, for example, the coefficient may be 0.1 and the correction amount may be 1.1 times, 1.2 times, etc.

[0187] Furthermore, while the above-described embodiment mentions an example of performing oxidation or diffusion treatment on the wafer 200, this disclosure is not limited thereto. For example, it may be a film deposition treatment such as CVD, and the type of film is not particularly limited. For example, it can be suitably applied when depositing various types of films, such as nitride films or metal oxide films, on the wafer 200. Needless to say, it can also be applied to various other treatments such as annealing and epitaxial growth.

[0188] Furthermore, this method can be applied not only to semiconductor manufacturing equipment that processes semiconductor wafers, such as the substrate processing apparatus according to the above embodiment, but also to LCD (Liquid Crystal Display) manufacturing equipment that processes glass substrates.

[0189] The disclosure of Japanese Patent Application No. 2024-168324, filed on 27 September 2024, is incorporated herein by reference in its entirety. All documents, patent applications, and technical standards described herein are incorporated herein by reference to the same extent as the individual documents, patent applications, and technical standards are incorporated herein by reference in the same manner as the individual documents, patent applications, and technical standards are incorporated herein by reference in the same manner as described herein.

Claims

1. A temperature control method that controls the power supplied to a heater so that a predicted temperature sequence calculated according to a pre-held prediction model approaches a future target temperature sequence, wherein the predicted temperature sequence is updated according to the prediction error between the current measured temperature (the temperature measured this time), the past measured temperature (the temperature measured in the past), and the current predicted temperature predicted in the past based on the predicted temperature sequence.

2. The temperature control method according to claim 1, wherein the predicted temperature sequence is used to calculate the future temperature when a constant power supply value is output to the heater controlled to a reference temperature in a steady state.

3. The temperature control method according to claim 1, wherein the predicted temperature sequence includes an individual input response characteristic matrix showing the amount of change influenced by the current furnace temperature and the current power supply value, and an individual zero response characteristic vector showing the amount of change influenced by past furnace temperatures and past power supply values.

4. The temperature control method according to claim 3, wherein the prediction error is configured to be reflected in the individual input response characteristic matrix.

5. The temperature control method according to claim 1, wherein the update of the predicted temperature series is performed every unit time.

6. The temperature control method according to claim 1, wherein the coefficients of the predicted temperature series are selected such that the next prediction error is smaller than the current prediction error.

7. The temperature control method according to claim 1, wherein the coefficients of the predicted temperature series are selected such that the prediction error decreases with each subsequent iteration.

8. The temperature control method according to claim 1, wherein the predicted temperature sequence includes a target temperature sequence vector in which the target values ​​of future temperature changes are expressed in vector form.

9. The temperature control method according to claim 8, comprising a ramp plate indicating a target temperature set for each future time point, a final target temperature, and a temperature change per unit time.

10. The temperature control method according to claim 1, wherein the prediction model includes coefficients for a prediction model that predicts at least one of the heater temperature and furnace temperature, a coefficient error correlation matrix, a reference temperature, and a steady-state power value.

11. The temperature control method according to claim 10, wherein the coefficients relating to the prediction model, the coefficient error correlation matrix, the reference temperature, and the steady-state power value are defined with respect to the heater temperature of each zone in the heater, which is divided into a plurality of regions, and the furnace temperature of each zone.

12. The temperature control method according to claim 1, wherein the prediction models for the heater temperatures of all zones and the furnace temperatures of all zones are all considered as a set and correspond to each temperature range.

13. The temperature control method according to claim 1, further comprising the steps of acquiring the prediction model, current and past data of the furnace temperature, and current and past data of the power supply value to the heater.

14. The temperature control method according to claim 11, further comprising the steps of calculating an individual input response characteristic matrix showing the amount of change influenced by the current furnace temperature and the current power supply value, an individual zero response characteristic vector showing the amount of change influenced by past furnace temperatures and past power supply values, and a target temperature column vector representing the target value of future temperature changes in vector form.

15. A temperature control method according to claim 14, comprising the steps of: creating an integrated characteristic equation consisting of an integrated input response characteristic matrix and an integrated zero response characteristic vector, and an integrated target temperature vector, by using the individual input response characteristic matrix, the individual zero response characteristic vector, and the target temperature column vector to integrate the characteristics in each zone; and optimizing the power supply value output to the heater by calculating a solution based on the integrated characteristic equation that minimizes the difference between the reference temperature and the predicted temperature.

16. A method for manufacturing a semiconductor device, comprising the step of processing a substrate while controlling the temperature inside a furnace to a processing temperature using the temperature control method described in any one of claims 1 to 15.

17. The method for manufacturing a semiconductor device according to claim 16, wherein the process comprises a plurality of steps including a heating step of raising the temperature to a processing temperature, a processing step of processing the substrate at the processing temperature, and a cooling step of lowering the temperature from the processing temperature to a predetermined temperature, and the prediction model can be set for each of the steps.

18. The method for manufacturing a semiconductor device according to claim 17, wherein the prediction model used in the heating step and the processing step is the same, and the prediction model used in the heating step and the processing step is different from the prediction model used in the cooling step.

19. A program executed in a substrate processing apparatus equipped with a control unit that controls the power supplied to a heater so that a predicted temperature sequence calculated according to a pre-held prediction model approaches a future target temperature sequence, the program causing the substrate processing apparatus to perform a procedure to update the predicted temperature sequence according to the prediction error between the current measured temperature (the temperature measured this time), the past measured temperature (the temperature measured in the past), and the past predicted current temperature calculated based on the predicted temperature sequence.

20. A substrate processing apparatus comprising: a substrate holder for holding multiple substrates; a reaction tube housing the substrate holder and constituting a processing chamber inside; a heater provided outside the reaction tube for heating the substrates held by the substrate holder; and a control unit that controls the power supplied to the heater so that a predicted temperature sequence calculated according to a pre-held prediction model approaches a future target temperature sequence, wherein the control unit is configured to update the predicted temperature sequence according to the error between the current measured temperature (the temperature measured this time), the past measured temperature (the temperature measured in the past), and the current predicted temperature predicted in the past based on the predicted temperature sequence.

Images