Controller for rapid heat treatment chambers based on machine learning models

Abstract

The embodiments disclosed in this specification include a method for developing a reduced-order model (ROM) for a model-based controller. In one embodiment, the method includes obtaining a design drawing of a plant and constructing a detailed model of the thermal network of the plant from the design drawing of the plant. In one embodiment, the method further includes obtaining a training input recipe and using the training input recipe to execute the detailed model. In one embodiment, the method further includes generating a plurality of snapshots, each snapshot including the temperatures of a plurality of components within the detailed model, and utilizing a dynamic mode decomposition control (DMDc) operation to extract the ROM from the plurality of snapshots.

Description

[Technical Field]

[0001] Cross-reference of related applications This application claims priority to U.S. Patent Application No. 17 / 723,285, filed on 18 April 2022, the entire contents of which are incorporated herein by reference.

[0002] The embodiment relates to the field of semiconductor manufacturing, and more specifically to a model-based controller that uses dynamic mode-decomposition control (DMDc) to generate a reduced-order model (ROM). [Background technology]

[0003] Description of related technologies Controllers are used to adjust measurement parameters within semiconductor processing tools. For example, a controller may be used to adjust the temperature of a substrate in a rapid heat treatment (RTP) tool. Generally, some controller architectures, such as PID controllers, are not well-suited for multiple-input multiple-output (MIMO) systems. RTP tools are an example of such a MIMO system. Therefore, the control of such systems has generally relied on what is classified as a model-based controller. In a model-based controller, a model of the system is developed that constitutes the control dynamics underlying the system. At the first level, a model-based controller can utilize a detailed model of the system (detailed model). However, such detailed models are often complex and require too much computing power to function as a proper real-time controller. Furthermore, such models may frequently need modification due to various factors such as parameter variability, manufacturing and assembly differences, and operational uncertainties and errors. Therefore, so-called reduced-order models (ROMs) are generated from detailed models.

[0004] In some cases, ROMs are extracted from solvers, such as detailed models. However, it's important to understand that not all stakeholders have access to these solvers. For example, solvers may be monopolized by companies that sell controller systems. Therefore, methods for generating ROMs that do not burden users have been proposed. [Overview of the project]

[0005] Embodiments described herein include methods for developing a reduced-order model (ROM) for a model-based controller. In one embodiment, the method includes obtaining a plant blueprint and constructing a detailed model of the plant's thermal network from the plant blueprint. In one embodiment, the method further includes obtaining a training input recipe and running the detailed model using the training input recipe. In one embodiment, the method further includes generating a plurality of snapshots, each snapshot containing the temperatures of a plurality of components in the detailed model, and utilizing a dynamic mode-decomposition control (DMDc) operation to extract the ROM from the plurality of snapshots.

[0006] The embodiments further include a processing tool. In one embodiment, the processing tool comprises a chamber, a plurality of lamps in the lid of the chamber, a reflector along the bottom of the chamber, and a substrate support that holds the substrate between the plurality of lamps and the reflector. In one embodiment, the processing tool includes a controller coupled to the chamber for controlling the temperature of the substrate, the controller being a model-based controller that utilizes a reduced-order model (ROM) generated in a dynamic mode-resolved control (DMDc) process.

[0007] Embodiments may further include a method for developing a reduced-order model (ROM) for a model-based controller. In one embodiment, the method includes generating a plurality of snapshots, each snapshot containing the temperatures of a plurality of components in a processing tool, and utilizing a dynamic mode-decomposition control (DMDc) operation to extract the ROM from the plurality of snapshots. [Brief explanation of the drawing]

[0008] [Figure 1] This is a schematic diagram of a system having a model-based controller according to one embodiment. [Figure 2] This diagram visually illustrates the process of using dynamic mode decomposition control (DMDc) to generate a reduced-order model (ROM). [Figure 3] This is a process flow diagram illustrating the operations used to generate a ROM using DMDc according to one embodiment. [Figure 4A] This is a schematic diagram of a rapid heat treatment (RTP) tool segmented into individual components to form a detailed model of the system according to one embodiment. [Figure 4B] In one embodiment, this is a training input recipe which is a graph of the normalized power supplied to one of the heater zones of the RTP tool. [Figure 4C] This is a graph of the normalized temperatures of various components in an RTP tool used to generate multiple snapshots used in the implementation of DMDc operations, according to one embodiment. [Figure 5] A block diagram of an exemplary computer system that may be used in conjunction with a processing tool, according to one embodiment, is shown. [Modes for carrying out the invention]

[0009] The systems described herein include a model-based controller using dynamic mode-decomposition control (DMDc) for generating a reduced-order model (ROM). Numerous specific details are presented in the following description to provide a comprehensive understanding of the embodiments. Those skilled in the art will see that embodiments can be carried out without these specific details. In other cases, well-known embodiments are not described in detail to avoid unnecessarily obscuring the embodiments. Furthermore, it should be understood that the various embodiments shown in the accompanying figures are illustrative and not necessarily drawn to scale.

[0010] As mentioned above, model-based controllers are typically used to control multiple-input multiple-output (MIMO) processes. One such MIMO process is the control of substrate temperature in rapid heat treatment (RTP) tools. Such tools are equipped with multiple lamps. In some cases, the lamps may be organized into two or more zones (e.g., an inner zone, an intermediate zone, and an outer zone) on the chamber lid. A reflector plate may be provided on the bottom of the chamber. The substrate may be positioned between the lamps and the reflector plate. In such a configuration, the control of various zones can be multiple inputs, and the substrate temperature at various locations can be multiple outputs.

[0011] In FIG. 1, a control system 100 for a plant 110 is shown. In FIG. 1, the plant 110 may be an RTP tool. However, it should be understood that the plant 110 may be any MIMO type of tool. For example, a furnace, an oven, a thermochemical plant, etc. can be used as the plant 110. In one embodiment, a control effort input u(t) (e.g., lamp power) is generated by a controller 112 and supplied to the plant 110. The state X(t) is the state of the components of the plant (i.e., temperature). A measurement tool 114 (e.g., one or more pyrometers) measures one or more temperatures of the components of the plant 110. The measured temperature Y(t) is compared with a setpoint temperature R(t), and an error signal e(t) is provided. The error signal e(t) is fed back to the controller 112.

[0012] In a particular embodiment, the controller 112 is a model-based controller (MBC). In one embodiment, the MBC uses a model that is the relationship between the control effort u(t) and the output Y(t). Usually, the model is based on a set of simultaneous equations of Equation 1, where B, D, and P are matrices used to model the system. TIFF0007886427000001.tif12170

[0013] However, in a system where radiation is dominant (e.g., an RTP tool), non-linear simultaneous equations may be more suitable. For example, the governing equations of heat transfer where radiation is dominant typically include a linear term in temperature (i.e., conduction and convection) and a quartic term (i.e., radiation). Therefore, the X 4 term can be included in the simultaneous equations. For example, Equation 2 is an example of such an embodiment, where A, B, D, and P are matrices and c is a constant. TIFF0007886427000002.tif13170

[0014] MIMO systems such as RTP tools are complex and have a wide substrate temperature range (e.g., from 400 °C to 1100 °C), so it is difficult to obtain a model like the above equation with conventional system identification methods. Therefore, the embodiments disclosed herein include the use of dynamic mode decomposition control (DMDc) to generate unknown matrices for model execution. In some embodiments, the DMDc method generates a system of linear equations (similar to Equation 1), and in other embodiments, the DMDc method generates a system of linear equations (similar to Equation 2).

[0015] For reference, the DMDc method is initiated after collecting dynamic data from either experiments or numerical simulations. The output data of the system is collected as n state values at m + 1 time steps. The time steps are assumed to be constant. This "snapshot" of the data is split into two parts, offset by one time step. The data at time step j, x j , the actuation input, u j and the data at the next time step x j+1 is sought for the linear relationship between the data. Equation 3 is as follows. TIFF0007886427000003.tif7170Here, x j is a column vector of length n in the system, the number of states, or the unknowns, and u j is a column vector of length l, the number of inputs or actuations to the system. In a numerical model, n is the number of nodes or cells into which the computational domain is divided and data is stored. This can range from dozens in a simple network type model to hundreds of thousands to millions in a two - or three - dimensional geometric model. Similarly, for a dataset from a numerical model, l is the number of volume and external boundary conditions that do not participate in the state variable x. For example, in a thermal system, this vector is the external component of the heat source, boundary heat flux, or convective and radiative heat flux conditions at the boundary nodes or cells that change over time.

[0016] The DMDc method allows us to obtain a simplified, low-dimensional representation of a numerical model. Instead of using the large and time-consuming original numerical model, this low-dimensional representation can be used to quickly analyze transient changes in the system. Assuming data with m+l time steps, the partitioned snapshot data matrix and the working matrix can be arranged as shown in Equation 4. TIFF0007886427000004.tif50170 Here, TIFF0007886427000005.tif6170 and TIFF0007886427000006.tif5170. The relationship in Equation 3 can be expressed as follows. TIFF0007886427000007.tif9170 Here, TIFF0007886427000008.tif5170 and TIFF0007886427000009.tif6170. The matrix Ω contains both state and input snapshot information. Next, to solve matrices A and B, least squares regression is performed using the generalized inverse matrix with the help of singular value decomposition (SVD) and degree reduction of Ω, as shown in Equation 6. TIFF0007886427000010.tif5170 Here, TIFF0007886427000011.tif6170, TIFF0007886427000012.tif6170, TIFF0007886427000013.tif4170, TIFF0007886427000014.tif6170, TIFF0007886427000015.tif5170, and TIFF0007886427000016.tif5170. amount TIFF0007886427000017.tif5170, TIFF0007886427000018.tif5170, and TIFF0007886427000019.tif5170 represents a truncated array with q singular values, retaining only the dominant mode of the system. Below are approximations of G, and A, and B. TIFF0007886427000020.tif6170TIFF0007886427000021.tif8170

[0017] Here, TIFF0007886427000022.tif7170 and TIFF0007886427000023.tif7170 and TIFF0007886427000024.tif8170. For large systems with hundreds of thousands or more states n, using these approximate A and B matrices in the prediction model of Equation 3 becomes extremely expensive. Therefore, TIFF0007886427000025.tif5170 and TIFF0007886427000026.tif5170 is further reduced in order using projection for such a system. The projected space is obtained using the SVD of the output space. The eigenvalues ​​and modes of the system are: TIFF0007886427000027.tif5170 and Extracted using the order reduction form of TIFF0007886427000028.tif5170. The dominant mode is typically selected to retain more than approximately 95% of the energy in the system. The energy corresponds to the sum of the singular values, or the sum of the squares of those values. After sorting the singular values ​​in descending order, the first q modes are selected and retain most of the system's energy. However, it should be understood that there are other processes for determining the dominant mode.

[0018] In one embodiment, the above-described DMDc method can be further modified to more accurately model the system behavior with nonlinear terms. For example, if temperature is a state data variable When TIFF0007886427000029.tif is 7170, the governing equation of heat transfer dominated by radiation usually includes a linear term (for conduction and convection) and a quartic term (for radiation), and T 4 provides variables. This applies when the material properties and thermal properties are constant across the computational domain. Accordingly, the x 4 term can be added to the DMDc equation.

[0019] The operating vector u j represents terms of boundary conditions and volume conditions that do not include the state data variable T in relation to the numerical model. These terms can represent, for example, a constant volume heat source term, a conduction or convection energy flux in the external region, or a radiative energy flux to or from the surroundings. The numerical model can have many such boundary conditions, most of which can be constant over time. It is not necessary to list and track all such terms in the operating vector u j and it can even be cumbersome.

[0020] Therefore, this vector u j is formed only from the non-state-dependent part that changes over time among the volume conditions and boundary conditions of the numerical model. To account for the remaining terms that are constant over time among such conditions, a constant term is further added to the DMDc equation. Adding the quartic term and the constant term, the modified equation is as follows. TIFF0007886427000030.tif9170 Here, σ’ is a scaling parameter based on the Stefan-Boltzmann constant of radiation and is pre-multiplied to make the numerical scales of matrices A1 and A2 the same. The vector g is a vector of size n×l with all elements being 1. Matrices A1, A2, C TIFF0007886427000031.tif4170. The term TIFF0007886427000032.tif7170 and C represent terms of non-linear conditions and constant boundary conditions, and / or volume conditions, respectively.

[0021] Next, a similar process is performed to extract the unknown matrices A1, A2, B, and C. TIFF0007886427000033.tif20170 Here, J is a matrix of size nxm where all elements are 1. θ = The SVD of TIFF0007886427000034.tif5170 TIFF0007886427000035.tif6170, TIFF0007886427000036.tif6170, TIFF0007886427000037.tif4170, TIFF0007886427000038.tif6170, TIFF0007886427000039.tif5170, and Let's assume the filename is TIFF0007886427000040.tif5170. Then, it will be as follows: TIFF0007886427000041.tif6170 and TIFF0007886427000042.tif17170

[0022] As before, here, It is TIFF0007886427000043.tif8170, and along with that, TIFF0007886427000044.tif7170, TIFF0007886427000045.tif7170, TIFF0007886427000046.tif7170 and The file is TIFF0007886427000047.tif7170. The modified method is expected to yield higher accuracy for systems with more states. Such systems will have more boundary and volume conditions. As a result, even if the operation vector consists only of a heat source term or boundary heat flux term that changes over time, the other terms of the original system are better represented by the approximate model from DMDc which has constant terms.

[0023] It will be understood that the most dominant mode identified by the modified DMDc method still derives from the linear matrix A1 in Equation 9. Therefore, the dominant patterns in the system are still recognized in the same way as in the original DMDc method. An additional term (A2) is added to the original DMDc primarily to aid in the fitting of the recognized system to the physical properties typically associated with radiant thermal systems. These additional terms also help ensure the stability of the system, since the eigenvalues ​​of the system in Equation 9 can be conveniently placed in the stable region by fine-tuning the constant σ'.

[0024] The mathematical process for extracting the ROM using standard DMDc and DMDc with polynomial expansion is as described above. Furthermore, Figure 2 illustrates the method for determining the ROM. As shown, X is equal to matrix 220. Matrix 220 contains multiple snapshots 221. Each snapshot 221 contains the temperatures of multiple components and the board within the RTP tool. Matrix 220 is then used to generate a system identification 222. The system identification 222 is, It takes the form TIFF0007886427000048.tif7170. However, it should be understood that in some embodiments, polynomial expansions can also be used. Matrices A and B of system identification 222 can be analogous to the matrix [AB] in equation 8. That is, for large systems with hundreds of thousands or more states n, using matrix [AB] becomes extremely expensive.

[0025] Therefore, the system identification 222 is morphological It can be further reduced to ROM223 which has TIFF0007886427000049.tif7170. In ROM223, A r Matrix and B r The matrix is ​​the matrix described in Equation 8. This may be similar to TIFF0007886427000050.tif7170. A r and B r The order is reduced using projection. As described in more detail above, the projected space is obtained using the SVD of the output space.

[0026] Figure 2 shows the extraction of the matrix into ROM states, but it should be understood that in some embodiments, the system identification 222 can be sufficiently simplified for use as a model for a model-based controller. For example, if the complexity of the system being modeled is reduced, it may not be necessary to further reduce the matrix to a complete ROM, as shown in Figure 2.

[0027] Furthermore, ROM is It is shown in the format TIFF0007886427000051.tif7170, but in other embodiments, Please understand that ROMs may contain polynomial formatting, such as TIFF0007886427000052.tif7170. The polynomial format of a ROM is a governing equation underlying the system, and T 4 This may be beneficial in radiation-dominated processes that include terms. The formation of polynomial ROM can be carried out using the same DMDc method as described in detail above for equations 9-12.

[0028] Referring now to Figure 3, a process flow diagram is shown illustrating a method 350 for forming a ROM according to one embodiment. The illustrated process involves the formation of a ROM using a numerical model. That is, multiple snapshots are captured using thermal simulation of the plant (e.g., an RTP tool). However, experimental data that similarly provides multiple snapshots is also used. Please understand that ROMs can also be developed.

[0029] In one embodiment, method 350 may begin with operation 351, which includes obtaining a model of the plant. In one embodiment, the plant model may be a computer-aided design (CAD) file containing each component of the plant. The CAD file may be generated before the plant is actually constructed. That is, a functional plant is not required before performing method 350. This makes it easier to modify components to improve the thermal control of the system. In one embodiment, the plant may be an RTP tool. However, it should be understood that in other embodiments, any thermal system can be modeled as a plant. For example, the plant may further include ovens, furnaces, thermochemical plants, etc.

[0030] In one embodiment, method 350 may then proceed to operation 352, which involves constructing a detailed computational thermal network simulation or model (i.e., a detailed model) of the plant. The detailed model may include several nodes that interact with each other thermally (e.g., via conduction, convection, and / or radiation). An example of a detailed model is shown in Figure 4A.

[0031] As shown in Figure 4A, the plant 460 has a chamber side wall 461 A and 461 B Includes. Side wall 461 A and 461 B Although it is modeled as discrete nodes, please note that the side walls 461 of the chamber may be made of a single material. A reflector plate 462 is provided at the bottom of the plant 460. Multiple heater zones 463 are located at the top of the plant 460. A-C There is a heater zone, which may be a circular annular plate. Each heater zone 463 may include one or more lamps configured to heat the substrate 465.

[0032] The substrate 465 is the heater zone 463 A-CIt can be positioned between the reflector plate 462. In the illustrated embodiment, for simplicity, the substrate 465 is shown as floating. However, it should be understood that a substrate support (not shown) may be provided below the substrate 465. In the illustrated embodiment, the substrate 465 is heated only by radiation because it is not in contact with other components of the plant 460. However, in practice, a conduction term may be included to consider an underlying support that is in contact with the substrate 465. In the illustrated embodiment, the substrate 465 is connected to multiple nodes 466 1-n It is divided into six nodes. For example, Figure 4A contains 6 nodes 466 1-6 This is shown. Three nodes 466 1-3 It is located on the top surface of the substrate 465, and there are three nodes 466 4-6 This is located on the bottom surface of substrate 465. Therefore, Figure 4A shows a total of 12 nodes (i.e., 6 nodes for substrate 465, 3 nodes for the heater zone, 1 node for the reflector, and 2 nodes for the side wall).

[0033] The equations for heat transfer between components can be derived using the surface-to-surface radiation method. Theoretical formulas for the radiation shape coefficient between circular disks, annular rings, and cylindrical surfaces can be used to model the thermal response of Plant 460. Furthermore, it should be understood that the thermal response shown in Figure 4A is considerably simplified for illustrative purposes. In practice, CAD files can provide sufficient detail to generate hundreds or even thousands of nodes. It should be understood that increasing the number of nodes does not negatively impact the model-based controller, as the detailed model is reduced to ROM using the DMDc method described in more detail above.

[0034] Referring again to Figure 3, method 350 may then proceed to operation 353. Operation 353 includes calibrating the detail model. The detail model can be calibrated by comparing the output of the numerical detail model with actual experimental data obtained when using plant 460. However, in some embodiments, plant 460 may not be available (for example, plant 460 may not be assembled). In such embodiments, the detail model may be used without calibration.

[0035] In one embodiment, method 350 may begin with operation 354, which includes developing a training input routine. The training input routine may include a recipe with various ramp-up, dwell time, and ramp-down values. Figure 4B is a graph of normalized power for one of the heater zones of plant 460. As shown, the training input routine is provided with a randomized distribution of ramp-up rates, dwell time, and ramp-down rates. A single heater zone is shown in Figure 4B. However, it should be understood that the training input routine may also include randomized power inputs for other heater zones. For example, individual heater zones may include different routines. Although the ramp-up, ramp-down, and dwell time are randomized, it should be understood that the various peaks should roughly capture the expected ramp rates, dwell time, etc., that will actually be implemented in the processing of the boards within plant 460.

[0036] Referring again to Figure 3, method 350 may then proceed to operation 355. Operation 355 further includes running the detailed model using the training input routine. That is, the detailed model is run at the power input of the training input routine. Because the detailed model can be complex, the real time required to run the training input routine may be longer than the time of the training input routine. That is, the detailed model may not be capable of performing real-time analysis of the plant. Therefore, ROM is required for it to function properly as a model-based controller.

[0037] In one embodiment, method 350 may proceed to operation 356, which includes recording the temperatures of all components (states) to obtain a data snapshot matrix. For example, a detailed model may output multiple snapshots at uniform time intervals. For example, each snapshot is provided at time intervals of one second or less. In some embodiments, the time interval may be less than one-tenth of a second. Each snapshot contains temperature data for each node of the detailed model. For example, Figure 4C shows the normalized temperatures of multiple nodes over a period of time. Although Figure 4C is depicted as a graph for ease of understanding, it should be understood that snapshots can be represented in matrix form, where the number of rows is equal to the number of nodes and the number of columns is equal to the number of snapshots.

[0038] Referring again to Figure 3, method 350 may then proceed to operation 357. Operation 357 involves using the DMDc method to extract the ROM. In some embodiments, the DMDc method may be a linear model similar to the equation shown in Equation 3. In other embodiments, the DMDc method may be a modified method that includes polynomial terms, such as the equation shown in Equation 9. The DMDc method may be carried out according to any of the embodiments described in more detail above. Generally, the process follows the flow shown in Figure 2. That is, a snapshot matrix 220 can be obtained, and a system identification 222 can be extracted from the snapshot matrix 220. If the system identification 222 is too complex to be performed as part of a model-based controller, the ROM 223 is extracted from the system identification 222.

[0039] The extracted ROM can then be used in a model-based controller, such as the model-based controller shown in Figure 1. That is, it can supply an error signal e(t) to the controller 112. Next, the controller 112 can use the ROM to generate a control signal u(t) that is supplied to the plant 110 to converge the measured temperature value Y(t) to a set temperature R(t).

[0040] The applicants developed a ROM according to the embodiments described in more detail above. In particular, such a ROM has been shown to exhibit high uniformity with the numerical detail model. For example, several different recipes (e.g., with various initial conditions and operating inputs) were run in the detail model. The output of the detail model closely matched the output provided by the ROM, which is similar to the output described in more detail herein. In some cases, the error limit between the output of the detail model and the output of the ROM was within 10%. However, in many cases, the error between the output of the detail model and the output of the ROM was within 5%. Furthermore, as the number of boundary and volume conditions of the model increases, the constant term in Equation 9 is expected to further improve the accuracy of the predictions.

[0041] Referring here to Figure 5, a block diagram showing an exemplary computer system 500 of a processing tool is shown according to an embodiment. In one embodiment, the computer system 500 is connected to the processing tool and controls the processing within the processing tool. The computer system 500 may be connected to (e.g., networked) other machines in a local area network (LAN), intranet, extranet, or internet. In a client-server network environment, the computer system 500 may operate as a server or a client machine, or in a peer-to-peer (or distributed) network environment, it may operate as a peer machine. The computer system 500 may be a personal computer (PC), tablet PC, set-top box (STB), personal digital assistant (PDA), mobile phone, web appliance, server, network router, switch or bridge, or any machine capable of executing a set of instructions (sequential or different) that specify the actions performed by that machine. Furthermore, although only a single machine is shown as computer system 500, the term “machine” should be further interpreted to include any collection of machines (e.g., computers) that individually or in conjunction execute a set (or set) of instructions in order to carry out any one or more of the methods described herein.

[0042] The computer system 500 may include a computer program product or software 522 having a non-transient machine-readable medium on which instructions are stored, and these instructions may be used to program the computer system 500 (or other electronic device) to perform processing according to the embodiment. The machine-readable medium includes any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer). For example, the machine-readable (e.g., computer-readable) medium includes machine (e.g., computer)-readable storage media (e.g., read-only memory (ROM), random-access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, etc.), machine (e.g., computer)-readable transmission media (in the form of electrical, optical, acoustic, or other propagating signals (e.g., infrared signals, digital signals, etc.)), etc.

[0043] In one embodiment, the computer system 500 includes a system processor 502, main memory 504 (e.g., read-only memory (ROM), flash memory, synchronous DRAM (SDRAM), or rhombus DRAM (RDRAM), or other dynamic random access memory (DRAM)), static memory 506 (e.g., flash memory, static random access memory (SRAM), etc.), and secondary memory 518 (e.g., a data storage device), all of which communicate with each other via a bus 530.

[0044] The system processor 502 represents one or more general-purpose processing devices, such as a microsystem processor or a central processing unit. More specifically, the system processor may be a composite instruction set arithmetic (CISC) microsystem processor, a reduced instruction set arithmetic (RISC) microsystem processor, a very long instruction word (VLIW) microsystem processor, a system processor that executes other instruction sets, or a system processor that executes a combination of instruction sets. The system processor 502 may also be one or more special-purpose processing devices, such as an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a digital signal system processor (DSP), or a network system processor. The system processor 502 is configured to execute processing logic 526 for performing the operations described herein.

[0045] The computer system 500 may further include a system network interface device 508 for communicating with other devices or machines. The computer system 500 may further include a video display unit 510 (e.g., a liquid crystal display (LCD), a light-emitting diode display (LED), or a cathode ray tube (CRT)), an alphanumeric input device 512 (e.g., a keyboard), a cursor control device 514 (e.g., a mouse), and a signal generation device 516 (e.g., a speaker).

[0046] The secondary memory 518 may include a machine-accessible storage medium 532 (or, more specifically, a computer-readable storage medium) storing one or more sets of instructions (e.g., software 522) that embody any one or more of the methods or functions described herein. The software 522 may also reside, all or at least partially, in the main memory 504 and / or the system processor 502 while being executed by the computer system 500, and the main memory 504 and the system processor 502 may also constitute a machine-readable storage medium. The software 522 may be further transmitted and received over the network 520 via the system network interface device 508. In one embodiment, the network interface device 508 may operate using RF coupling, optical coupling, acoustic coupling, or inductive coupling.

[0047] In the exemplary embodiments, the machine-accessible storage medium 532 is shown as a single medium, but the term “machine-readable storage medium” should be understood to include a single medium or multiple mediums (e.g., a centralized or distributed database, and / or associated caches and servers) that store one or more sets of instructions. Furthermore, the term “machine-readable storage medium” should be interpreted to include any medium capable of storing or encoding a set of instructions executed by a machine, and causing the machine to execute one or more of the methods described above. Therefore, the term “machine-readable storage medium” should be interpreted to include, but not be limited to, solid memory, optical media, and magnetic media.

[0048] The above specification describes specific exemplary embodiments. It will be apparent that various modifications can be made to these exemplary embodiments without departing from the scope of the following claims. Therefore, this specification and the drawings should be considered illustrative, not limiting.

Claims

1. A method for developing a reduced-order model (ROM) for a model-based controller, To obtain the design plans for a plant that performs heating including thermal radiation, To construct a detailed model of the thermal network of the plant from the design drawings of the plant, Obtaining training input recipes, The detailed model is executed using the aforementioned training input recipe, The process involves generating multiple snapshots, each of which includes the temperatures of multiple components within the detailed model. To extract the ROM from the aforementioned multiple snapshots, a dynamic mode decomposition control (DMDc) operation is used. A method that includes this.

2. The method according to claim 1, further comprising calibrating the detailed model using available experimental data.

3. The method according to claim 1, wherein the DMDc operation includes a nonlinear component.

4. The aforementioned ROM, The method according to claim 3, wherein the format is such that A, B, and D are matrices.

5. The aforementioned ROM, The method according to claim 1, wherein the format is such that A and B are matrices.

6. The method according to claim 1, wherein the plant is a rapid heat treatment (RTP) tool.

7. The aforementioned RTP tool is Multiple heater zones in the chamber lid, and A reflector plate covering the bottom of the chamber. The method according to claim 6, comprising:

8. The method according to claim 1, wherein the ROM is an approximation of the actual governing equations of the thermodynamics of the plant.

9. The method according to claim 1, wherein the error between the output of the ROM and the output of the detailed model is within 10%.

10. The method according to claim 1, wherein the design drawing of the plant is a computer-aided design (CAD) file.

11. It is a processing tool, Chamber, Multiple lamps in the lid of the chamber, A reflector along the bottom of the chamber, A substrate support that holds the substrate between the plurality of lamps and the reflector, and A controller connected to the chamber for controlling the temperature of the substrate, which is a model-based controller that utilizes a reduced-order model (ROM) generated by a dynamic mode-decomposition control (DMDc) process. A processing tool equipped with these features.

12. The processing tool according to claim 11, wherein the processing tool is a rapid heat treatment (RTP) tool.

13. The aforementioned ROM, The processing tool according to claim 11, wherein the format is such that A and B are matrices.

14. The aforementioned ROM, The processing tool according to claim 11, wherein the format is such that A, B, and D are matrices.

15. The processing tool according to claim 11, wherein the ROM is generated from a plurality of snapshots.

16. The processing tool according to claim 15, wherein the ROM is generated before the processing tool is assembled.

17. The processing tool according to claim 11, wherein the ROM is an approximation of the actual governing equations of thermodynamics for the processing tool.

18. A method for developing a reduced-order model (ROM) for a model-based controller, The process involves generating multiple snapshots, each snapshot containing the temperatures of multiple components within a plant that perform heating, including thermal radiation. To extract the ROM from the aforementioned multiple snapshots, a dynamic mode decomposition control (DMDc) operation is used. Methods that include...

19. The generation of the aforementioned multiple snapshots is To obtain computer-aided design drawings of the aforementioned plant, To construct a detailed model of the thermal network of the plant from the computer-aided design drawings of the plant, Obtaining training input recipes, The detailed model is executed using the aforementioned training input recipe. The method according to claim 18, including the method described in claim 18.

20. The generation of the aforementioned multiple snapshots is Executing the training recipe on the aforementioned plant, Recording the temperature of multiple components at multiple times and The method according to claim 18, including the method described in claim 18.

21. The detailed model of the thermal network is at least One or more nodes for the heater zone in the lid of the chamber of the plant, One or more divided nodes for the upper surface of the substrate arranged in the chamber, One or more divided nodes for the lower surface of the substrate, One or more nodes for the side wall of the chamber, One or more nodes for the reflector of the chamber and The method according to claim 1, including the method described in claim 1.

22. The detailed model of the thermal network from which the ROM is extracted is based on a plurality of snapshots, the plurality of snapshots include the temperatures of a plurality of components of the processing tool, The detailed model described above includes at least, One or more nodes for the heater zone in the lid of the chamber of the processing tool, One or more divided nodes for the upper surface of the substrate arranged in the chamber, One or more divided nodes for the lower surface of the substrate, One or more nodes for the side wall of the chamber, One or more nodes for the reflector of the chamber and The processing tool according to claim 11, including the following:

23. The plurality of snapshots include the temperatures of a plurality of components in a detailed model of the thermal network of the plant, The detailed model described above includes at least One or more nodes for the heater zone in the lid of the chamber of the plant, One or more divided nodes for the upper surface of the substrate arranged in the chamber, One or more divided nodes for the lower surface of the substrate, One or more nodes for the side wall of the chamber, One or more nodes for the reflector of the chamber and The method according to claim 18, including the method described in claim 18.

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