Temperature control system, substrate heating method, semiconductor device manufacturing method, substrate processing device, and recording medium

Abstract

Provided is a technology comprising a heater that heats a plurality of zones, and a temperature control unit that controls power supplied to the heater such that a predicted temperature sequence calculated in accordance with a prediction model stored in advance approaches a future target temperature sequence. The prediction model for a specific zone from among the plurality of zones is corrected to update the predicted temperature sequence, the specific zone is heated by the heater on the basis of the updated predicted temperature sequence, and zones other than the specific zone from among the plurality of zones are heated by the heater on the basis of the original predicted temperature sequence.

Description

Temperature control system, substrate heating method, semiconductor device manufacturing method, substrate processing apparatus, and recording medium

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

[0002] In a substrate processing apparatus, a type of semiconductor manufacturing equipment, for example, a substrate is placed in a furnace and heated to form a thin film on the processing substrate. In such a furnace, temperature control may be performed taking into account the thermal interference from multiple heat sources to multiple temperature sensors. For example, as described in Japanese Patent Publication No. 2000-183072 or Japanese Patent Publication No. 2009-117798, feedback control using proportional-integral-derivative (PID) calculations may be performed based on a preset temperature to make the furnace follow a specified temperature change.

[0003] This disclosure provides a technology that maintains high temperature control performance inside a furnace, regardless of rapid changes in the set temperature.

[0004] According to one aspect of the present disclosure, a technology is provided comprising a heater for heating a plurality of zones, and a temperature 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 prediction model for a specific zone among the plurality of zones is modified to update the predicted temperature sequence, the heater is used to heat based on the updated predicted temperature sequence, and the zones among the plurality of zones excluding the specific zone are heated by the heater based on the predicted temperature sequence.

[0005] According to this disclosure, high temperature control performance inside the furnace can be maintained without rapid changes in the set temperature.

[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 storage area shown in Figure 3, and is a reference value for the prediction model of the furnace temperature in zone b, and is a figure showing the power supply amount for each zone when the furnace temperature in zone b is in a steady state at the reference temperature, with the reference temperature being 212°C. This figure shows another example of data stored in the prediction model storage 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. Figure 9A is a flowchart showing an example of a substrate processing process. This is a figure showing the change in furnace temperature in each processing step of Figure 9A. This figure shows the trajectory of the furnace temperature and power supply value by prediction temperature control according to a comparative example of the present disclosure. This is a figure showing the trajectory of the furnace temperature and power supply value by prediction temperature control according to one embodiment of the present disclosure in Figure 10A. This is a figure for explaining the modification of the prediction model according to one embodiment of the present disclosure, and is a flowchart showing the automatic acquisition procedure of thermal characteristics of the temperature control unit according to one embodiment of the present disclosure. This is a control block diagram of the inside of the temperature control unit in S308 and S312 shown in Figure 12.This is an internal control block diagram of a temperature control unit according to another embodiment of the present disclosure.

[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 pipe 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) via a gas flow controller. If it is necessary to supply steam into the processing chamber 201, a steam generator (not shown) is provided downstream of the MFC 241 on the gas supply pipe 232. 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 gases so that the pressure inside the processing chamber 201 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 inside the processing chamber 201 at a desired timing based on the pressure detected by the pressure sensor 245, using the pressure regulator 242 to achieve the desired pressure.

[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 temperature inside the processing chamber 201 is then raised 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. In this specification, processing temperature refers to the temperature of the wafer 200 or the temperature inside the processing chamber 201. Processing time refers to the time during which the processing is continued. These terms are also used in the following description. 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 inside the processing chamber 201 to reach the processing temperature set by the higher-level controller 36 at the desired timing.

[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 storage device consists of, for example, flash memory, HDD (Hard Disk Drive), SSD (Solid State Drive), etc. The storage device contains, in a readable format, a control program that controls the operation of the substrate processing device 10, and a process recipe that describes the procedures and conditions for the processing described later. The process recipe is a combination of steps in the processing described later that can be executed by the main control unit 240 to obtain a predetermined result, and functions as a program. Hereinafter, the process recipe and control program will be collectively referred to simply as a program (program product). Similarly, the process recipe will be simply referred to as a recipe. In this specification, the term "program" may include only a recipe, only a control program, or both.

[0035] The main control unit 240 can be configured by installing the above-mentioned program, which is recorded and stored on an external storage device (not shown) (for example, a magnetic disk such as a hard disk, an optical disk such as a CD (Compact Disk), or a semiconductor memory such as a USB (Universal Serial Bus) memory), into a computer. The storage unit and storage device are configured as computer-readable recording media. Hereinafter, these will be collectively referred to simply as recording media. In this specification, the term recording media may include only the storage unit, only the storage device, or both.

[0036] The temperature history storage area 850 stores the history of heater temperature data (heater temperature information), which is the heater temperature 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 inside the processing chamber 201 detected by the first temperature sensor 263 via the temperature input circuit 722, for a certain period of time.

[0037] 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. In this specification, numerical range notations such as "0 to 100%" mean that the lower limit and upper limit are included in that range. Therefore, for example, "0 to 100%" means "0% or more and 100% or less". The same applies to other numerical ranges.

[0038] 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.

[0039] Here, the reference temperature is the temperature at which the heater temperature and furnace temperature are in a steady state (hereinafter sometimes referred to as the processing temperature). The steady-state power value is the reference value of the prediction model, which is the power supply value for each zone when the heater temperature and furnace temperature are in a steady state at the reference temperature.

[0040] 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.

[0041] 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.

[0042] 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.

[0043] 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.

[0044] The parameter storage area 856 stores various parameters necessary to implement the prediction model.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] The display / input device 720 can display and input various parameters stored in the parameter storage area 856.

[0049] [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.

[0050] 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.

[0051] a1, a2, m ａ1 , ···, m ａn , m ｂ1 , ···, mb n , m ｃ1 , ···, m ｃn , m ｄ1 , ···, m ｄn , m ｅ1 , ···, m ｅn are the respective coefficients. b ｉ is the constant term. The n value is a value preset in the parameter storage area 856.

[0052] 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.

[0053] ] The prediction model is stored for each zone for each of the heater temperature and the furnace temperature and can be used for control calculation. Specifically, for example, a prediction model regarding the predicted temperature of the furnace temperature in zone a, a prediction model regarding 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.

[0054] The reference temperature and steady-state power values ​​are obtained in the automatic thermal characteristics acquisition procedure described later, prior to creating the predictive model. Constant term b ｉ This is an adjustment term for when the previously acquired reference temperature or steady-state power value deviates from the actual value. If the previously acquired reference temperature or steady-state power value remains constant over time, the constant term of the prediction model shown in Equation 1 obtained after the automatic acquisition procedure of thermal characteristics is b ｉ A value of 0 is expected. However, the reference temperature and steady-state power value change moment by moment due to changes in the surrounding environment, power fluctuations, thermocouple noise, etc., so these are included in the prediction model (Equation 1).

[0055] 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.

[0056] 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) = bi, so the predicted temperature = b + 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.

[0057] 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.

[0058] 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.

[0059] Furthermore, regarding the heater temperature prediction model, Equation 2 below may be used as a substitute to simplify the calculations.

[0060] 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.

[0061] 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 the thermal influence from the heaters 206 in the other divided zones is either nonexistent or negligibly small.

[0062] 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.

[0063] Figure 6 is a control block diagram of the internal temperature control unit 238 shown in Figure 3.

[0064] 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.

[0065] 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.

[0066] 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.

[0067] 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.

[0068] 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.

[0069] 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.

[0070] 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.

[0071] 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).

[0072] The above equation 1 can be expressed using a state-space model as shown in equation 3 below.

[0073] 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.

[0074] 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).

[0075] 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.

[0076] 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.

[0077] 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.

[0078] 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.

[0079] 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.

[0080] 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.

[0081] 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.

[0082] 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.

[0083] 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.

[0084] First, the individual input response characteristic matrix S srThe 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. Instead of holding u(t), different values ​​u(t) to u(t+N) are used at all control timings. ｐ If we input -1), the second term on the right-hand side of equation 4 becomes the following: where Np is the row number of equation 4.

[0085] In well-known model predictive control, different values ​​u(t) to u(t+N) occur at the timing of all calculations. ｐ Assuming that -1) is input, these are calculated to obtain the answer. However, since the 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.

[0086] Here, N ｃｄ is the number of input rows to be held in the first stage. The input u(t) of the first stage is set to time t+N ｃｄ Hold down to -1. The second input is u(t+N). ｃｄ ) is retained thereafter. As described above, the individual input response characteristic matrix S sr By rearranging equation 4, we obtain equation 6 as shown below.

[0087] 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.

[0088] Next, regarding equations 6 and 5 described above, we list all the zones to be controlled.

[0089] 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.

[0090] 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.

[0091] 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.

[0092] The power supply unit 718 then controls the amount of power supplied to the heater 206 to correspond to a power supply value between 0 and 100%.

[0093] Note that although there are as many limiters 812 and power supply units 718 as there are divisions in the heater, only one of each is shown in Figure 6 for simplicity.

[0094] [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.

[0095] 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.

[0096] In S201, a solution x within the range where the equal sign in Equation 10 is not valid is selected. And the set of rows where the equal sign becomes valid among each row of Equation 10 is defined as A, b. In S201, both A and b are empty sets. Also, the set of rows where the equal sign does not become valid among each row of Equation 10 is defined as A, b. In S201, A = A and b = b. k Then, a solution x and λ are obtained by solving the following system of linear equations. If x = x, proceed to S205. If x ≠ x, proceed to S207. e b e In S201, both A and b are empty sets. Also, the set of rows where the equal sign does not become valid among each row of Equation 10 is defined as A, b. In S201, A = A and b = b. e b e In S201, both A and b are empty sets. Also, the set of rows where the equal sign does not become valid among each row of Equation 10 is defined as A, b. In S201, A = A and b = b. d b d In S201, both A and b are empty sets. Also, the set of rows where the equal sign does not become valid among each row of Equation 10 is defined as A, b. In S201, A = A and b = b. d = A, b d = b.

[0097] In S203, the following system of linear equations is solved, and the solutions are x and λ. If x = x, proceed to S205. If x ≠ x, proceed to S207. k If so, proceed to S205. If x ≠ x k Then, proceed to S207.

[0098] In S205, it is determined 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.

[0099] In S207, α is obtained according to the following Equation 11. In Equation 10, b and a are each one row extracted from A and b. If α = 1, proceed to S205. If α < 1, proceed to S209. i a i are each one row extracted from A, b d b d respectively. If α = 1, proceed to S205. If α < 1, proceed to S209.

[0100] In S209, when α (< 1) is obtained according to Equation 11, the constraint {b, a} used is deleted from A, b and added to A, b, and then proceed to S203. i a i} is d b d deleted from A, b and added to A, b, and then proceed to S203. e b e In S209, when α (< 1) is obtained according to Equation 11, the constraint {b, a} used is deleted from A, b and added to A, b, and then proceed to S203.

[0101] In S211, the element of λ that is the minimum among negative values is selected, and the corresponding one {b, a} among the constraints included in A, b is deleted from A, b and added to A, b. e b e among the constraints included in A, b is i b i} is e b e deleted from A, b and added to A, b. d, b d Add to this and proceed to S203.

[0102] In S213, the solution x obtained in S203 is considered the optimal solution and the process terminates.

[0103] The effective constraint method shown in Figure 7 can find a solution that satisfies Equation 10 and maximizes Equation 9 by searching for combinations of rows in Equation 10 in which the equality is valid, using the accompanying multiplier λ.

[0104] [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.

[0105] 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.

[0106] 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.

[0107] 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.

[0108] 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 ａThese 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%.

[0109] [Second Effectiveness Constraint Method]

[0110] 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.

[0111] 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.

[0112] In S215, the loop count is initialized.

[0113] Then, in S217, the solution x in the range where the equality in equation 10 is not valid is obtained. k Select this option. 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, the power supply value P in zone a. a Regarding the constraint, 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.

[0114] 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.

[0115] 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.

[0116] [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.

[0117] 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.

[0118] In S300, the temperature control unit 238 controls the furnace temperature, and this process is repeated 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.

[0119] In S302, the temperature control unit 238 controls the furnace temperature, and this process is repeated until the furnace temperature is controlled to a reference temperature and a steady state is reached. At this time, the parameters used for control (for example, 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.

[0120] 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.

[0121] 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.

[0122] 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.

[0123] 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.

[0124] 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 repeated 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.

[0125] 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.

[0126] 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.

[0127] 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.

[0128] 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.

[0129] 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.

[0130] Next, the heater temperature prediction model update unit 836 obtains the prediction model for the heater temperature of the zone from the prediction model 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.

[0131] 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.

[0132] 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.

[0133] [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.

[0134] 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.

[0135] The coefficients θ(t) of the latest prediction model are calculated as shown in equation 28 below.

[0136] 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.

[0137] 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.

[0138] 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).

[0139] 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).

[0140] 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.

[0141] 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.

[0142] This was assumed to be the case where it is unstable.

[0143] 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.

[0144] 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).

[0145] 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.

[0146] [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.

[0147] 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.

[0148] 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.

[0149] 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.

[0150] 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.

[0151] 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,

[0152] And in the next second process...

[0153] And in the following third and subsequent processing...

[0154] 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.

[0155] Next, an example of a substrate processing sequence performed by the substrate processing apparatus 10 will be explained using Figures 9A and 9B.

[0156] 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.

[0157] 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.

[0158] Step S103 (stabilization step) is a step in which the furnace temperature is maintained and stabilized at the standby temperature T0.

[0159] 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.

[0160] 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, the above-described cooling step is performed.

[0161] 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 217.

[0162] If there are any unprocessed wafers 200 that need to be processed, the processed wafers 200 are removed from the boat 217 and replaced with the unprocessed wafers 200, and this series of processes from steps S101 to S106 is performed one or more times.

[0163] In step S104 (heating step) shown in Figure 9B, the temperature control unit 238 controls the current heater supply power so that the predicted temperature sequence calculated according to a pre-held furnace temperature prediction model approaches the future target temperature sequence, thereby raising the furnace temperature to the target temperature T １ By converging to this point, the recovery time from the heating step (step S104) to the processing step (step S105) can be shortened. 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).

[0164] Next, the embodiment shown in Figure 11 will be described below. In Figure 11, for the sake of clarity, there are three zones (U zone, C zone, and L zone). The L zone is an example of a "zone that does not face the space for processing the substrate in the furnace" in this disclosure, an example of a "zone that does not face the holder that holds the substrate", an example of a "zone that does not face the substrate", and an example of a "zone that does not face the temperature sensor placed in the space for processing the substrate".

[0165] Predictive temperature control is a multi-input, multi-output system. Therefore, in predictive temperature control, to track rapid changes in the set temperature, for example, if an adjacent zone (zone C) is overshooting, one of the causes is insufficient power supply to a specific zone (zone L). As a result, predictive temperature control increases the power supply to the adjacent zone (zone C) to improve the temperature rise delay in the specific zone (zone L). Consequently, predictive temperature control determines that even if there is some overshoot in the adjacent zone (zone C), it is optimal for the three-zone temperature control if the temperature rise of the specific zone (zone L) is faster. Therefore, predictive temperature control calculates the power supply value for the adjacent zone (zone C) while being strongly affected by the thermal influence (thermal interference) of the specific zone (zone L). In other words, it is unable to neutralize the thermal influence (thermal interference) of the specific zone (zone L) and calculates the power supply value for the adjacent zone (zone C).

[0166] Therefore, in this embodiment, as shown in Figure 11, the power supply value from the adjacent zone (zone C), which is susceptible to temperature fluctuations in other zones including a specific zone, to other zones is forcibly eliminated, thereby eliminating thermal interference from other zones (including the adjacent zone) to the adjacent zone (zone C). This forcibly suppresses the control operation that would improve the temperature rise delay caused by temperature fluctuations (temperature drop) from other zones, specifically, by increasing the power supply value to the adjacent zone (zone C) even if the power supply value to a specific zone is insufficient. Consequently, unnecessary power load is not placed on the adjacent zone (zone C), the temperature controllability of the adjacent zone (zone C) is improved, and overshoot can be eliminated.

[0167] Next, we will specifically explain the case of eliminating interference from a specific zone to an adjacent zone using the prediction model stored in the prediction model memory area 854. Here, the prediction model is a mathematical formula for calculating the predicted temperature, and uses Equation 1 described above. For example, the prediction model for a specific zone (zone L) is the coefficient m in the following equation. c1 ,m c2 ,・・・m cn By setting this to 0, interference from other zones to adjacent zones can be eliminated.

[0168] Let's take the example of calculating predicted temperatures assuming three zones (zones U, C, and L) as shown in Figure 11. Using Equation 1 described above, the formula for calculating the predicted temperature of zone U is explained below. The part U1・y(t-1) + U2・y(t-2) (corresponding to the first line of Equation 1 above) represents the effect on zone U of the deviation of the temperature one and two cycles prior to zone U from the reference temperature. mU1・pU(t-1) + mU2・pU(t-2)・・mU n The part pU(tn) (corresponding to the second line of equation 1 above) is the interference (influence) on zone U by the power supply value uU from zone U itself one cycle prior, two cycles prior, and n cycles prior. mC1・pC(t-1) + mC2・pC(t-2)・・mC n The part pC(tn) (corresponding to the third line of Equation 1 above) is the interference (influence) on zone U by the power supply value uC from zone C one, two, and n times prior. Here, the coefficients of zone C are mC1, mC2, ... mC n By setting this to 0, mC1・pC(t-1) + mC2・pC(t-2)・・mC n - The pC(tn) portion becomes 0, meaning that interference (influence) on zone U (a specific zone) due to the power supply value from zone C (an adjacent zone) is not considered (dotted arrow from uC to yU in Figure 11). mL1・pL(t-1) + mL2・pL(t-2)・・mL nThe part pL(tn) (corresponding to the 4th line (effectively the last line) of Equation 1 above) represents the interference (influence) on Zone U by the power supply value uL from Zone L one, two, and n times prior. When calculating the predicted temperature and determining the power supply value uU for Zone U, interference from Zone C is not considered; in other words, as shown by the dotted line in Figure 11, it can be assumed that the interference (influence) of Zone U's control calculation on Zone C's power supply value uC is eliminated. As shown by the dotted line in Figure 11, it can be assumed that Zone L (a specific zone) is similar to Zone U in that Zone L's control calculation on Zone C's power supply value uC is eliminated. On the other hand, since only interference from zones adjacent to a specific zone is eliminated here, interference from Zone L is taken into consideration when calculating the predicted temperature and determining the power supply value uU for Zone U. Also, interference from Zone U is taken into consideration when calculating the predicted temperature and determining the power supply value uL for Zone L.

[0169] On the other hand, when calculating the predicted temperature of the adjacent zone itself, the coefficient mU1 ... mU n Do not set it to 0. As shown in Figure 11, by considering the influence (arrows) from zones U and L on zone C and calculating the predicted temperature of the adjacent zone (zone C), it is possible to eliminate the influence of the temperature of other zones on the power supply value uC of zone C while ensuring the predictive control accuracy of zone C itself. In this way, the prediction model is corrected, and the temperature control unit 238 calculates the power supply value so that the predicted temperature sequence created by the corrected prediction model matches the target temperature sequence given by the higher-level controller 36.

[0170] (Example) Figure 10 shows the temperature inside the furnace and the power supply value when the temperature is controlled by the temperature control unit 238 during the heating process (step S104). Figure 10A shows a graph when predictive temperature control is performed in a comparative example, and Figure 10B shows a graph when predictive temperature control is performed in one embodiment of the present disclosure. Figure 10 describes the heating process (step S104), but it goes without saying that this embodiment is not limited to this process. Also, in Figure 10, the trajectories of other zones are omitted except for a specific zone and the zone adjacent to this specific zone (hereinafter referred to as the adjacent zone). Note that there may be multiple zones adjacent to a specific zone, as long as they are thermally affected by the specific zone. Here, an adjacent zone is the zone that is most susceptible to thermal influence (thermal interference) because it is adjacent to the specific zone.

[0171] Figure 10A shows the predicted temperature control using the temperature control unit 238, which has already been explained, and the explanation of this predicted temperature control will be omitted. As shown in Figure 10A, in a specific zone, the temperature rises in line with the set temperature in response to changes in the set temperature, and the temperature detection value can be quickly made to follow the set temperature. On the other hand, as shown in Figure 10A, the power supply value of the adjacent zone is overloaded due to thermal influence from the specific zone, and the temperature of the adjacent zone is overshooting the target temperature.

[0172] In Figure 10B, the temperature in the adjacent zone does not exceed the target temperature, and overshoot is suppressed. On the other hand, because the power supply value to the adjacent zone is effectively suppressed, the temperature rise time relative to the set temperature is delayed compared to Figure 10A, but the ability to follow the set temperature is still ensured.

[0173] As shown in Figures 10A and 10B, the time required to stabilize at the target temperature is determined by the zone that has a significant impact on adjacent zones due to temperature fluctuations, i.e., a specific zone in this embodiment, and therefore remains virtually unchanged.

[0174] Furthermore, the temperature control unit 238 according to this embodiment can reduce overshoot and minimize inter-zone deviations. Also, even when there is significant variation in the individual temperature characteristics of the heaters, or when the assigned engineer does not have sufficient time, the thermal characteristics can be automatically acquired, and the optimal control method can be obtained without parameter adjustment, or by easily adjusting the parameters. Therefore, the expected performance of the device can be easily obtained.

[0175] Although embodiments of this disclosure have been described in detail above, this disclosure is not limited to the embodiments and examples described above, and can be modified in various ways without departing from its essence.

[0176] Figure 14 is an internal control block diagram of the temperature control unit 238 according to another embodiment of the present disclosure. The difference from the internal control block diagram of the temperature control unit 238 shown in Figure 6 is that a PID control unit 238b and a power output determination unit 811 have been added, and a limiter 812 and a power supply unit 718 have been provided after the power output determination unit 811. In addition, the parameter storage area 856 stores not only various parameters for realizing the prediction model, but also various parameters used in PID control calculations. In addition, the program storage area 726 stores a temperature control program for prediction that selects a prediction model in a predetermined temperature range, inputs temperature data, and controls the temperature so that the predicted temperature is optimal, as well as a temperature control program for PID used in PID control calculations.

[0177] In Figure 14, the predictive temperature control unit 238a controls the heater 206 by obtaining temperature history, power supply value history, and various parameters from the temperature history storage area 850, power supply value history storage area 852, and parameter storage area 856, respectively, in accordance with the determination of the power output determination unit 811, and executing a predictive temperature control program using the predictive model stored in the predictive model storage area 854. The predictive temperature control unit 238a is configured to execute a predictive temperature control program that includes at least the following steps: a procedure to obtain temperature data of at least one of the following: the heater temperature, which is the temperature of the heater 206, and the furnace temperature, which is the temperature of the processing chamber 201, and the power supply value to the heater 206; a procedure to obtain a predictive model from the predictive model storage area 854 that predicts a reference temperature for the temperature data and a predicted temperature for the temperature data; a procedure to calculate the power supply value using the predictive model so as to minimize the difference between the reference temperature and the predicted temperature; and a procedure to output the power supply value and control the heating of the heater 206. Furthermore, the temperature control program for prediction is configured to include a procedure for creating a characteristic equation using a prediction model and a procedure for calculating the solution to the characteristic equation. Meanwhile, the PID control unit 238b, in response to the determination of the power output determination unit 811, obtains PID parameters from the parameter storage area 856 and executes the temperature control program for PID, thereby controlling the heater 206 by performing feedback control using proportional, integral, and differential (hereinafter referred to as PID) calculations based on a preset target temperature.

[0178] The temperature control unit 238 shown in Figure 14 includes at least a temperature control performed by a prediction control unit 238a as a first temperature control, which controls the temperature inside the furnace based on the respective temperatures detected in multiple zones; a temperature control performed by a PID control unit 238b as a second temperature control, which controls the temperature inside the furnace based on the temperature detected in one of the multiple zones; and a power output determination unit 811 that selects and controls either the first temperature control unit or the second temperature control unit for each zone. The system is configured to heat a specific zone among the multiple zones with a heater based on the second temperature control, and heat the zones excluding the specific zone with the heater based on the first temperature control.

[0179] With this configuration, in predictive temperature control, even if the power supply value to a specific zone (zone L in Figure 11) is insufficient to follow rapid changes in the set temperature, the power output determination unit 811 can select a temperature control method different from predictive temperature control for each zone. This allows for individual control of zones that are susceptible to thermal influence from a specific zone. As a result, temperature control within the processing furnace 202 becomes possible without adjacent zones being affected by the temperature in a specific zone, and an improvement in temperature uniformity between wafers 200 can be expected.

[0180] Furthermore, the above-described embodiment explained an example in which a predetermined process is performed on the wafer 200. This disclosure is not particularly limited to the process, and may include, for example, a film deposition process 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 and metal oxide films, on the wafer 200. Needless to say, it can also be applied to various other processes such as annealing and epitaxial growth.

[0181] 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.

[0182] The disclosure of Japanese Patent Application No. 2024-168879, 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 system comprising: heaters for heating multiple zones; and a temperature control unit that controls the power supplied to the heaters to bring a predicted temperature sequence calculated according to a pre-held prediction model closer to a future target temperature sequence, wherein the temperature control unit is configured to update the predicted temperature sequence by modifying the prediction model for a specific zone among the multiple zones, heat the heaters based on the updated predicted temperature sequence, and heat the zones excluding the specific zone among the multiple zones based on the predicted temperature sequence.

2. The temperature control system according to claim 1, wherein the specific zone is a zone in which the temperature rise due to heating by the heater is delayed compared to other zones.

3. The temperature control system according to claim 1, wherein the specific zone is a zone in which the power supply value is insufficient to follow the change in the set temperature.

4. The temperature control system according to claim 1, wherein the specific zone is the zone with the lowest position among the plurality of zones.

5. The temperature control system according to claim 2, wherein the modification of the prediction model for the specific zone is to set the coefficients applied to the prediction model to zero.

6. The temperature control system according to claim 5, wherein the coefficient relating to the zone that is thermally affected by the specific zone is set to zero.

7. The temperature control system according to claim 6, wherein the zone that is thermally affected by the specific zone is a zone adjacent to the specific zone.

8. For the specific zone, the temperature control unit calculates an individual input response characteristic matrix showing the amount that changes in the predicted temperature vector, which is obtained by modifying the prediction model and representing the updated predicted temperature sequence in vector form, due to the influence of the power supply value calculated this time, and an individual zero response characteristic vector showing the amount that changes in the predicted temperature vector due to the influence of past furnace temperatures and past power supply values, according to claim 1.

9. For zones excluding the specified zone, the temperature control unit calculates an individual input response characteristic matrix showing the amount of change in the predicted temperature vector, which is a vector representation of the predicted temperature sequence, that is influenced by the power supply value calculated this time, and an individual zero response characteristic vector showing the amount of change in the predicted temperature vector that is influenced by past furnace temperatures and past power supply values, according to claim 8.

10. The temperature control unit is configured to further perform the following processes: creating an integrated characteristic equation using the individual input response characteristic matrix, the individual zero response characteristic vector, and the target temperature sequence vector representing the future target temperature sequence in vector form; and inputting the integrated input response characteristic matrix, the integrated zero response characteristic vector, the integrated target temperature vector, and the upper and lower limit values ​​of each zone calculated in the process of creating the integrated characteristic equation, and calculating the current power supply value using the effective constraint method with respect to the integrated characteristic equation.

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

12. The temperature control system according to claim 11, wherein at least one of the coefficients, coefficient error correlation matrix, reference temperature, and steady-state power value relating to the prediction model is defined with respect to the heater temperature of each zone and the furnace temperature of each zone, respectively.

13. The temperature control system 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.

14. The temperature control system according to claim 1, wherein the specific zone is a zone among the plurality of zones that does not face the space in the furnace where the substrate is processed.

15. The temperature control system according to claim 1, wherein the specific zone is a zone among the plurality of zones that does not face a holder for holding a substrate.

16. The temperature control system according to claim 15, wherein the specific zone is a zone among the plurality of zones that does not face the substrate.

17. The temperature control system according to claim 1, wherein the specific zone is a zone among the plurality of zones that does not face a temperature sensor located in the space for processing the substrate.

18. A substrate heating method comprising the step of bringing the inside of a furnace to a processing temperature using the temperature control system described in any one of claims 1 to 17.

19. 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 a temperature control system according to any one of claims 1 to 17.

20. A substrate processing apparatus comprising: heaters for heating multiple zones; and a temperature control unit that controls the power supplied to the heaters so that a predicted temperature sequence calculated according to a pre-held prediction model approaches a future target temperature sequence, wherein the temperature control unit is configured to update the predicted temperature sequence by modifying the prediction model for a specific zone among the multiple zones, heat the zones with the heaters based on the updated predicted temperature sequence, and heat the zones excluding the specific zone with the heaters based on the predicted temperature sequence.

21. A computer-readable recording medium containing a temporarily recorded program executed by the substrate processing apparatus according to claim 20.

Images