Controller for a rapid heat treatment chamber based on a machine learning model

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 to Related Applications This application claims priority to U.S. Patent Application No. 17 / 723,285, filed on April 18, 2022, the entire content of which is incorporated herein by reference.

[0002] Embodiments relate to the field of semiconductor manufacturing, and more particularly, to a model - based controller that uses dynamic mode decomposition control (DMDc) to generate reduced order models (ROMs).

Background Art

[0003] Description of Related Art Controllers are used to adjust measurement parameters within semiconductor processing tools. For example, a controller can be used to adjust the temperature of a substrate in a rapid thermal processing (RTP) tool. Generally, some controller architectures, such as a PID controller, are not well - suited for multi - input multi - output (MIMO) systems. An RTP tool is an example of such a MIMO system. Thus, 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 that constitutes the underlying control dynamics of the system is developed. At a first level, the model - based controller can utilize a detailed model of the system (detailed model). However, such detailed models are often complex and require too much computational power to operate as a suitable real - time controller. Further, such models may frequently need to be corrected due to various factors such as parameter variations, manufacturing and assembly differences, operational uncertainties, and errors. Thus, so - called reduced order models (ROMs) are generated from the detailed models.

[0004] In some cases, the ROM is extracted from a solver such as a detailed model. However, it should be understood that not all stakeholders can access the solver. For example, the solver may be exclusive to a company that sells controller systems. Therefore, a method for generating ROM without imposing a burden on users has been proposed.

Summary of the Invention

[0005] The embodiments described herein 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.

[0006] The embodiments further include a processing tool. In one embodiment, the processing tool includes a chamber, a plurality of lamps in the lid of the chamber, a reflector along the bottom of the chamber, and a substrate support for holding a substrate between the plurality of lamps and the reflector. In one embodiment, the processing tool includes a controller connected to the chamber for controlling the temperature of the substrate, and the controller is a model-based controller that utilizes a reduced-order model (ROM) generated by a dynamic mode decomposition 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 including the temperatures of a plurality of components within a processing tool, and applying a dynamic mode decomposition control (DMDc) operation to extract the ROM from the plurality of snapshots.

Brief Description of the Drawings

[0008]

Figure 1

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Figure 4A

Figure 4B

Figure 4C

Figure 5

Best Mode for Carrying Out the Invention

[0009] The system described in this specification includes a model-based controller that uses dynamic mode decomposition control (DMDc) to generate a reduced-order model (ROM). In the following description, numerous specific details are presented in order to provide a comprehensive understanding of the embodiments. It will be apparent to those skilled in the art that the embodiments can be practiced without these specific details. In other instances, well-known aspects are not described in detail so as not to obscure the embodiments needlessly. Further, it should be understood that the various embodiments shown in the accompanying figures are exemplary representations and are not necessarily drawn to scale.

[0010] As described above, model-based controllers are typically used to control multi-input multi-output (MIMO) processes. One such MIMO process is the control of substrate temperature in a rapid thermal processing (RTP) tool. In such a tool, multiple lamps are provided. In some cases, the lamps can be arranged in two or more zones (e.g., an inner zone, a middle zone, and an outer zone) on the lid of the chamber. A reflector plate can be provided on the bottom surface of the chamber. The substrate can be positioned between the lamps and the reflector plate. In such a structure, the control of the various zones can be multiple inputs, and the temperatures of the substrate at various positions 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 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 the system of simultaneous equations of Equation 1, where B, D, and P are matrices used to model the system. TIFF2025516124000002.tif12170

[0013] However, in a system where radiation is dominant (e.g., an RTP tool), a system of 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 terms can be included in the system of 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. TIFF2025516124000003.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 and 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 determined. Equation 3 is as follows. TIFF2025516124000004.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 where the data is stored. This can range from dozens in a simple network type model to hundreds of thousands to millions in a two-dimensional 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] Using the DMDc method, a simplified low-dimensional representation of the numerical model can be obtained. Instead of using the original large-scale and time-consuming numerical model, this low-dimensional representation can be used to quickly analyze the transient changes of the system. Assuming the data of m + l time steps, the divided snapshot data matrix and the operation matrix can be arranged as shown in Equation 4. TIFF2025516124000005.tif50170 Here, TIFF2025516124000006.tif6170 and TIFF2025516124000007.tif5170. The relationship in Equation 3 can be expressed as follows. TIFF2025516124000008.tif9170 Here, TIFF2025516124000009.tif5170 and TIFF2025516124000010.tif6170. Matrix Ω includes both state and input snapshot information. Next, to solve for matrix A and matrix B, least squares regression using the general inverse matrix is performed with the help of the singular value decomposition (SVD) of Ω and order reduction. As shown in Equation 6. TIFF2025516124000011.tif5170 Here, TIFF2025516124000012.tif6170, TIFF2025516124000013.tif6170, TIFF2025516124000014.tif4170, TIFF2025516124000015.tif6170, TIFF2025516124000016.tif5170, and TIFF2025516124000017.tif5170. The quantity TIFF2025516124000018.tif5170, TIFF2025516124000019.tif5170, and TIFF2025516124000020.tif5170 represents a truncated array with q singular values and retains only the dominant mode of the system. The following are approximations of G, and A, B. TIFF2025516124000021.tif6170TIFF2025516124000022.tif8170

[0017] Here, TIFF2025516124000023.tif7170 and TIFF2025516124000024.tif7170 and TIFF2025516124000025.tif8170. For large-scale systems with hundreds of thousands or more states n, using these approximate A and B matrices in the prediction model of Equation 3 is prohibitively expensive. Therefore, TIFF2025516124000026.tif5170 and TIFF2025516124000027.tif5170 are further reduced in degree using projections for such systems. The projection space is obtained using the SVD of the output space. The eigenvalues and modes of the system are TIFF2025516124000028.tif5170 and TIFF2025516124000029.tif5170 are extracted using a reduced-degree form. The dominant modes are typically selected to retain more than about 95% of the energy within the system. The energy corresponds to the sum of the singular values, or the sum of their squared values. After arranging the singular values in descending order, the first q modes are selected to retain most of the energy of the system. However, it should be understood that there are other processes for determining the dominant modes.

[0018] In one embodiment, the above DMDc method can be further modified to more accurately model the behavior of the system with non-linear terms. For example, temperature is a state data variable When TIFF2025516124000030.tif7170, 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 a variable. 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, in the context of the numerical model, terms of boundary conditions and volume conditions that do not include the state data variable T. 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, and even cumbersome, to list and track all such terms in the operating vector u j Therefore, this vector u

[0020] is formed only from the non-state-dependent parts of the volume and boundary conditions of the numerical model that change over time. 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. j TIFF2025516124000031.tif9170 Here, σ’ is a scaling parameter based on the Stefan-Boltzmann constant of radiation and is pre-multiplied to equalize the numerical scales of the matrices A and A 1 and A 2 The vector g is a vector of size n×l with all elements equal to 1. The matrices A 1 and A 2 and C TIFF2025516124000032.tif4170. The term TIFF2025516124000033.tif7170 and C represent terms of non-linear conditions and constant boundary conditions, and / or volume conditions, respectively.

[0021] Next, for the unknown matrix A 1 A 2 Similar processing is performed to extract A, B, and C. TIFF2025516124000034.tif20170 Here, J is a matrix of size nxm with all elements equal to 1. θ = Perform the SVD of TIFF2025516124000035.tif5170 TIFF2025516124000036.tif6170, TIFF2025516124000037.tif6170, TIFF2025516124000038.tif4170, TIFF2025516124000039.tif6170, TIFF2025516124000040.tif5170, and TIFF2025516124000041.tif5170. Then, it becomes as follows. TIFF2025516124000042.tif6170 and TIFF2025516124000043.tif17170

[0022] As before, here TIFF2025516124000044.tif8170, and together with TIFF2025516124000045.tif7170, TIFF2025516124000046.tif7170, TIFF2025516124000047.tif7170 and TIFF2025516124000048.tif7170. The modified method can be expected to provide high accuracy for systems with more states. Such systems will have more boundary conditions and volume conditions. As a result, even if the operating vector is composed only of a heat source term or a boundary heat flux term that changes over time, the other terms of the original system can be better represented by an approximate model from DMDc with constant terms.

[0023] It should be understood that the most dominant modes identified by the modified DMDc method still originate from the linear matrix A in Equation 9. 1 Therefore, the main patterns within the system are still recognized in the same way as the original DMDc method. Mainly, additional terms (A 2 ) are added to the original DMDc to assist in the recognized system's conformity to the physical properties typically associated with radiative heat transfer systems. These additional terms also help ensure the stability of the system. This is because the eigenvalues of the system in Equation 9 can be conveniently arranged in the stable region by finely tuning the constant σ'.

[0024] The mathematical process of extracting the ROM using standard DMDc and DMDc with polynomial expansion is as described above. Additionally, Figure 2 illustrates the method of determining the ROM. As shown, X is equal to matrix 220. Matrix 220 includes a plurality of snapshots 221. Each snapshot 221 includes the temperatures of a plurality of components and substrates within the RTP tool. Then, matrix 220 is used to generate system identification 222. System identification 222 takes the form of TIFF2025516124000049.tif7170. However, it should be understood that in some embodiments, polynomial expansion can also be used. The matrices A and B of system identification 222 can be similar to the matrix [AB] in Equation 8. That is, in a large-scale system with hundreds of thousands or more states n, using the matrix [AB] would be prohibitively expensive.

[0025] Therefore, system identification 222 is in the form It can be further reduced to the ROM223 having TIFF2025516124000050.tif7170. In ROM223, A r matrix and B r matrix are the matrices described in Equation 8 It may be similar to TIFF2025516124000051.tif7170. A r and B r are reduced in degree using projection. As described in more detail above, the projection space is obtained using the SVD of the output space.

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

[0027] Furthermore, the ROM is shown in the format of TIFF2025516124000052.tif7170. However, in other embodiments, it should be understood that it may include a ROM in polynomial format such as TIFF2025516124000053.tif7170. The polynomial format of the ROM is beneficial in a radiative dominant process that includes T 4 terms in the governing equation underlying the system. The formation of the polynomial ROM can be performed using a DMDc method similar to that shown in detail with respect to Equations 9-12 described in more detail above.

[0028] Referring now to FIG. 3, a process flow diagram showing a method 350 for forming a ROM according to an embodiment is shown. The illustrated process involves the formation of a ROM using a numerical model. That is, a plurality of snapshots are captured using a thermal simulation of a plant (e.g., an RTP tool). However, experimental data that provides a plurality of snapshots in a similar manner can also be used, It should be understood that the ROM can also be developed.

[0029] In one embodiment, method 350 may start with operation 351. Operation 351 includes obtaining a model of the plant. In one embodiment, the model of the plant may be a computer-aided design (CAD) file that includes each component of the plant. The CAD file can be generated before the plant is actually constructed. That is, there is no need for a functional plant before executing method 350. Therefore, it becomes easy to modify components to improve the thermal control of the system. In one embodiment, the plant may be an RTP tool. However, in other embodiments, it should be understood that any thermal system can be modeled as a plant. For example, the plant may further include an oven, a furnace, a thermochemical plant, etc.

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

[0031] As shown in FIG. 4A, plant 460 includes chamber sidewalls 461 A and 461 B The sidewalls 461 A and 461 B are modeled as discrete nodes, but it should be understood that the sidewalls 461 of the chamber may be of a single material. A reflector plate 462 is provided at the bottom of plant 460. There are a plurality of heater zones 463 A-C at the top of plant 460. The heater zones may be circular annular plates. Each heater zone 463 may include one or more lamps configured to heat a substrate 465.

[0032] The substrate 465 is the heater zone 463A-C and 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 since there is no contact with other components of the plant 460. However, in practice, a conduction term may be included considering the underlying support in contact with the substrate 465. In the illustrated embodiment, the substrate 465 is divided into a plurality of nodes 466 1-n For example, FIG. 4A shows six nodes 466 1-6 Three nodes 466 1-3 are on the upper surface of the substrate 465, and three nodes 466 4-6 are on the bottom surface of the substrate 465. Thus, in FIG. 4A, a total of twelve nodes (i.e., six nodes for the substrate 465, three nodes for the heater zone, a node for the reflector, and two nodes for the side walls) are shown.

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

[0034] Referring back to FIG. 3, method 350 may then proceed to operation 353. Operation 353 includes calibrating the detailed model. The detailed model can be calibrated by comparing the output of the numerical detailed model with the actual experimental data obtained during the use of plant 460. However, in some embodiments, plant 460 may not be available (e.g., plant 460 may not be assembled). In such embodiments, the detailed model may be used without calibration.

[0035] In one embodiment, method 350 may start at operation 354. Operation 354 includes developing a training input routine. The training input routine may include recipes that include various ramp-ups, dwell times, and ramp-downs. FIG. 4B is a graph of the normalized power for one of the heater zones of plant 460. As shown, the training input routine provides a random classification of ramp-up rate, dwell time, and ramp-down rate. A single heater zone is shown in FIG. 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 times are randomized, it should be understood that the various peaks should approximately capture the expected ramp rates and dwell times, etc. that are actually implemented in the processing of the substrates within plant 460.

[0036] Referring back to FIG. 3, method 350 may then proceed to operation 355. Operation 355 further includes executing the detailed model using the training input routine. That is, the detailed model is executed with the power inputs of the training input routine. Since the detailed model can be complex, the real time required for the execution of 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, a ROM is required to function properly as a model-based controller.

[0037] In one embodiment, method 350 may subsequently proceed to operation 356. Operation 356 includes recording the temperatures of all components (states) to obtain a data snapshot matrix. For example, a detailed model can output multiple snapshots at uniform time intervals. For example, each snapshot is provided at a time interval of 1 second or less. In some embodiments, the time interval may be less than one-tenth of a second. Each snapshot includes temperature data for each node of the detailed model. For example, in FIG. 4C, the normalized temperatures of multiple nodes are shown over a certain period. Although FIG. 4C is depicted as a graph for ease of understanding, it should be understood that the snapshots can be represented in matrix form with the number of rows equal to the number of nodes and the number of columns equal to the number of snapshots.

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

[0039] The extracted ROM can then be used in a model-based controller such as the model-based controller shown in FIG. 1. That is, an error signal e(t) can be supplied to controller 112. Next, controller 112 can use the ROM to generate a control signal u(t) that is supplied to plant 110 to converge the measured temperature value Y(t) to the 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 have a high degree of uniformity with numerical detailed models. For example, a plurality of different recipes (e.g., having various initial conditions and operating inputs) were executed in the detailed model. The output of the detailed model was in exact conformity with the output provided by a ROM similar to the output described in more detail herein. In some cases, the error limit between the output of the detailed model and the output of the ROM was within 10%. However, in many cases, the error between the output of the detailed model and the output of the ROM was within 5%. Furthermore, as the number of boundary conditions and volume conditions of the model increases, the constant term in Equation 9 is expected to further enhance the accuracy of the prediction.

[0041] Referring now to FIG. 5, a block diagram showing an exemplary computer system 500 of a processing tool is shown in accordance with an embodiment. In one embodiment, the computer system 500 is coupled to the processing tool and controls the processing within the processing tool. The computer system 500 can be connected (e.g., networked) to other machines in a local area network (LAN), intranet, extranet, or the Internet. The computer system 500 can operate in the role of a server or client machine in a client-server network environment, or can operate as a peer machine in a peer-to-peer (or distributed) network environment. The computer system 500 can be any machine capable of executing a set of (sequential or otherwise) instructions that specify the actions to be taken by that machine, such as a personal computer (PC), tablet PC, set-top box (STB), personal digital assistant (PDA), cellular phone, web appliance, server, network router, switch or bridge, or the like. Further, although only a single machine is shown as the computer system 500, the term "machine" should be further construed to include any collection of machines (e.g., computers) that individually or jointly execute a set of (or multiple sets of) instructions to perform 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-transitory machine-readable medium storing instructions that may be used to program a computer system 500 (or other electronic device) to perform the processing according to the embodiments. 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 a machine (e.g., computer) readable storage medium (e.g., read-only memory (ROM), random access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, etc.), a machine (e.g., computer) readable transmission medium (in the form of electrical, optical, acoustic, or other propagated signals (e.g., infrared signals, digital signals, etc.)), and the like.

[0043] In one embodiment, the computer system 500 includes a system processor 502, a main memory 504 (e.g., dynamic random access memory (DRAM) such as read-only memory (ROM), flash memory, synchronous DRAM (SDRAM), or Rambus DRAM (RDRAM)), a static memory 506 (e.g., flash memory, static random access memory (SRAM), etc.), and a secondary memory 518 (e.g., a data storage device), 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 micro system processor or a central processing unit. More specifically, the system processor can be a complex instruction set computing (CISC) micro system processor, a reduced instruction set computing (RISC) micro system processor, a very long instruction word (VLIW) micro system processor, a system processor that executes other instruction sets, or a system processor that executes a combination of instruction sets. The system processor 502 can 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) in which one or more sets of instructions (e.g., software 522) embodying any one or more of the methods or functions described herein are stored. The software 522 may also reside, in whole or at least in part, within 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 embodiment, 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 media (e.g., a centralized database or a distributed database, and / or associated caches and servers) that store one or more sets of instructions. Further, the term "machine-readable storage medium" should be interpreted to include any medium that is capable of storing or encoding a set of instructions executable by a machine and that causes a machine to execute any one or more of the methods. Thus, the term "machine-readable storage medium" should be interpreted to include, but not be limited to, solid-state memory, optical media, and magnetic media.

[0048] In the foregoing specification, specific exemplary embodiments have been described. It will be apparent that various modifications may be made to the specific exemplary embodiments without departing from the scope of the following claims. Accordingly, the specification and drawings are to be regarded in an illustrative rather than a limiting sense.

Claims

1. A method for developing a reduced-order model (ROM) for a model-based controller, comprising: obtaining a design drawing of a plant; constructing a detailed model of the thermal network of the plant from the design drawing of the plant; obtaining a training input recipe; executing the detailed model using the training input recipe; generating a plurality of snapshots, each snapshot including temperatures of a plurality of components within the detailed model; utilizing a dynamic mode decomposition control (DMDC) operation to extract the ROM from the plurality of snapshots and a method comprising the above.

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 non-linear components.

4. The ROM is in the format of , where A, B, and D are matrices, and the method according to claim 3.

5. The ROM is in the format of , where A and B are matrices, and the method according to claim 1.

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

7. The RTP tool includes a plurality of heater zones in the lid of the chamber, and a reflector plate covering the bottom of the chamber and the method according to claim 6.

8. The method according to claim 1, wherein the ROM is an approximation of the actual governing equation 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. A processing tool comprising: a chamber; a plurality of lamps in the lid of the chamber; a reflector along the bottom of the chamber; a substrate support for holding a substrate between the plurality of lamps and the reflector; and a controller connected 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 by a dynamic mode decomposition control (DMDC) process and a processing tool comprising the above.

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

13. The ROM is in the format of, where A and B are matrices, the processing tool according to claim 11.

14. The ROM is in the format of, where A, B, and D are matrices, the processing tool according to claim 11.

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

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

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

18. A method for developing a reduced-order model (ROM) for a model-based controller, comprising: generating a plurality of snapshots, each snapshot including temperatures of a plurality of components within a processing tool; utilizing a dynamic mode decomposition control (DMDC) operation to extract the ROM from the plurality of snapshots and.

19. Generating the plurality of snapshots includes obtaining a computer-aided design drawing of a plant; constructing a detailed model of the thermal network of the plant from the computer-aided design drawing of the plant; obtaining a training input recipe; executing the detailed model using the training input recipe and, the method according to claim 18.

20. Generating the plurality of snapshots includes executing a training recipe on a processing tool; recording the temperatures of a plurality of components at a plurality of times and, the method according to claim 18.

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