Information processing method, computer program, and information processing device

Abstract

The invention provides an information processing method, a computer program, and an information processing apparatus which are expected to effectively utilize data obtained from a substrate processing apparatus. According to the information processing method of the embodiment, the information processing apparatus acquires time-series observation data obtained by observing the state of the substrate processing apparatus, and calculates parameters of a model by dynamic mode decomposition based on the acquired time-series observation data. The model predicts, on the basis of first observation information relating to observation data at a first time, second observation information relating to observation data at a second time after the first time.

Description

Technical Field

[0001] The present disclosure relates to an information processing method, a computer program, and an information processing apparatus. Background Art

[0002] In Patent Document 1, a state determination apparatus is proposed that acquires data related to industrial machinery, and based on the acquired data related to industrial machinery, generates a plurality of partial time series data obtained by sliding the time series data of physical quantities in the data related to industrial machinery in the time axis direction, extracts a plurality of learning data including the plurality of partial time series data, and generates a learning model by performing machine learning using the extracted learning data.

[0003] Patent Document 1: Japanese Unexamined Patent Application Publication No. 2020 - 128013 Summary of the Invention

[0004] The present disclosure provides an information processing method, a computer program, and an information processing apparatus that can be expected to effectively utilize data obtained from a substrate processing apparatus.

[0005] An information processing method according to an embodiment is processed by an information processing apparatus as follows: acquiring time series observation data obtained by observing the state of a substrate processing apparatus, and calculating parameters of a model based on the acquired time series observation data by dynamic mode decomposition, where the model is a model for predicting second observation information related to observation data at a second time after the first time based on first observation information related to observation data at the first time.

[0006] Advantages of the Invention

[0007] According to the present disclosure, it is possible to expect effective utilization of data obtained from a substrate processing apparatus. Brief Description of the Drawings

[0008] Figure 1 It is a schematic diagram for explaining the outline of the information processing system according to the present embodiment.

[0009] Figure 2 It is a block diagram showing a configuration example of the information processing apparatus according to the present embodiment.

[0010] Figure 3 It is a flowchart showing an example of the process of the abnormality determination process performed by the information processing apparatus according to the present embodiment.

[0011] Figure 4 It is a graph showing an example of time series observed temperature data.

[0012] Figure 5 It is a graph showing an example of internal state data obtained by dynamic mode decomposition.

[0013] Figure 6 It is a heat map showing an example of the matrix U obtained by dynamic mode decomposition.

[0014] Figure 7 It is a flowchart showing an example of the process of information display processing performed by the information processing apparatus of the present embodiment.

[0015] Figure 8 It is a schematic diagram for explaining the outline of the information processing system of the modification example.

[0016] Figure 9 It is a schematic diagram for explaining the method of acquiring the control input data and the observed temperature data of the information processing apparatus of Modification 2. Detailed Embodiments

[0017] Hereinafter, specific examples of the information processing system according to the embodiments of the present disclosure will be described with reference to the drawings. Note that the present disclosure is not limited to these examples, but is represented by the claims, and is intended to include all modifications within the meaning and scope equivalent to the claims.

[0018] <System Outline>

[0019] Figure 1 It is a schematic diagram for explaining the outline of the information processing system of the present embodiment. The information processing system of the present embodiment is configured to include an information processing apparatus 1 and a substrate processing apparatus 3. The illustrated substrate processing apparatus 3 is, for example, a processing chamber or the like for performing processing such as etching on a semiconductor wafer. The substrate processing apparatus 3 includes an electrostatic chuck 3a for electrostatically fixing, for example, a wafer to be processed, a cooler (cooling device) and / or a heater (heating device) or the like as a temperature control device for controlling the temperature of the wafer (not shown), and a sensor for measuring the temperature of the wafer (not shown).

[0020] The information processing apparatus 1 is a device for controlling and monitoring the operation of the substrate processing apparatus 3. In the present embodiment, the temperature of the substrate processing apparatus 3 is controlled. The information processing apparatus 1 is connected to the substrate processing apparatus 3 via, for example, a communication line or a signal line, provides control input data to the temperature control device of the substrate processing apparatus 3, and acquires observed temperature data obtained by the sensor of the substrate processing apparatus 3. The information processing apparatus 1 determines the control input data based on the observed temperature data acquired from the substrate processing apparatus 3, and provides the control input data to the temperature control device of the substrate processing apparatus 3. Thereby, the temperature of the wafer fixed to the electrostatic chuck 3a of the substrate processing apparatus 3 is controlled to maintain a desired temperature.

[0021] In addition, in the present embodiment, when the information processing apparatus 1 performs processing on a wafer by the substrate processing apparatus 3, for example, the control input data and the observed temperature data are sampled and acquired at a predetermined frequency such as once per second or once per minute. The information processing apparatus 1 stores the acquired control input data and observed temperature data in a database. Further, in the present embodiment, the information processing apparatus 1 inputs a plurality of control values as control data to the temperature control apparatus of the substrate processing apparatus 3. Also, a plurality of temperature sensors are provided in the substrate processing apparatus 3 to observe the temperature distribution of the wafer, and the information processing apparatus 1 acquires the temperatures at multiple locations of the wafer measured by the plurality of temperature sensors as observed temperature data. Therefore, in the present embodiment, the control input data and the observed temperature data stored in the database by the information processing apparatus 1 are respectively multi-dimensional (two-dimensional or more) vector information. The dimensions of the control input data and the observed temperature data may not be equal. Further, either or both of the control input data and the observed temperature data may be one-dimensional scalar values.

[0022] In the present embodiment, after the processing on the wafer is completed, for example, the information processing apparatus 1 determines the presence or absence of an abnormality in the processing on the wafer or the operation of the substrate processing apparatus 3, etc. based on the time series data of the control input data and the observed temperature data stored in the database. Also, when an abnormality is detected, for example, the information processing apparatus 1 performs various information displays based on the time series data stored in the database in order to assist the user in analyzing the cause of the abnormality, etc.

[0023] In the present embodiment, the information processing apparatus 1 uses the method of "dynamic mode decomposition" in order to perform the determination of the presence or absence of the above-mentioned abnormality and information display, etc. Dynamic mode decomposition is a method of decomposing time series data into a plurality of variation factors (modes), and can generate a model for generating predicted time series data by using the method of dynamic mode decomposition. The generated model is a model that accepts, for example, the observed data at a certain moment as input and outputs the predicted value of the observed data at the next moment. The information processing apparatus 1 can determine the parameters of the model that outputs the predicted value by performing the processing of dynamic mode decomposition by using the time series data stored in the database. Among them, dynamic mode decomposition is a known analysis method (for example, refer to "Jonathan H. Tu, Clarence W. Rowley, Dirk M. Luchtenburg, Steven L. Brunton, J. Nathan Kutz. On dynamic mode decomposition: Theory and applications. Journal of Computational Dynamics, 2014, 1(2): 391 - 421."), so the detailed description is omitted.

[0024] For example, in Figure 1 In the example shown, the information processing device 1 performs "dynamic mode decomposition" processing based on the time-series observed temperature data obtained by the sensor of the substrate processing device 3. Thus, the information processing device 1 can generate a model that accepts the observed temperature data at a certain moment as input and outputs the predicted value of the observed temperature data at the next moment. In addition, the model generated by the information processing device 1 does not necessarily have to be a model that takes the observed temperature data obtained from the substrate processing device 3 as input and output. The model can also take, as input and output, data obtained by performing some arithmetic processing (pre-processing) on the observed temperature data, such as the average value or the differential value of the observed temperature data. For example, the model can be configured to accept the average value of the observed temperature data within a specified time range at a certain moment and the previous moments as input and output the predicted value of the average value of the observed temperature data at the next moment and within the specified time range at the previous moments. Also, for example, the model can be configured to accept the first-order differential value of the observed temperature data at a certain moment as input and output the predicted value of the first-order differential value of the observed temperature data at the next moment. Additionally, the forms of the input information and the output information of the model can be different. For example, the model can be configured to accept the average value of the observed temperature data at a certain moment as input and output the predicted value of the first-order differential value of the observed temperature data at the next moment.

[0025] Furthermore, in the present embodiment, the information processing device 1 uses a method of "dynamic mode decomposition with control input" that can append the time-series data of the processing control input to the dynamic mode decomposition. The information processing device 1 can generate a model that accepts, as input, for example, the control input data and the observed temperature data at a certain moment and outputs the predicted value of the observed temperature data at the next moment by using the method of dynamic mode decomposition with control input. In addition, the method of dynamic mode decomposition with control input is a known analysis method (for example, refer to "Dynamic mode decomposition with control" by Joshua L. Proctor, Steven L. Brunton, J. Nathan Kutz, September 24, 2014), and detailed description is omitted.

[0026] In the present embodiment, the information processing device 1 performs a process of "dynamic mode decomposition with control input" based on, for example, control input data to the substrate processing device 3 and observed temperature data from the substrate processing device 3. Thereby, the information processing device 1 can generate a model that receives control input data and observed temperature data at a certain time as inputs and outputs a predicted value of the observed temperature data at the next time. In addition, the control input data input to the model, like the model that outputs the predicted value of the observed temperature data, is data obtained by performing some arithmetic processing on the data input to the substrate processing device 3, such as an average value or a first-order differential value. Further, in the following description, even when only "dynamic mode decomposition" is described, it includes this "dynamic mode decomposition with control input".

[0027] The information processing device 1 performs dynamic mode decomposition with control input based on the control input data and the observed temperature data that are acquired and stored in the database when the substrate processing device 3 processes one wafer. Thereby, the information processing device 1 can obtain the values of the internal parameters of a model that receives control input data and observed temperature data at a certain time as inputs and outputs a predicted value of the observed temperature data at the next time. The information processing device 1 compares the parameters of the obtained model with, for example, the parameters of a model determined using data collected for wafers that have been processed normally or the parameters of a model determined using data collected when an abnormality occurs during processing. Thereby, the information processing device 1 can determine the presence or absence of an abnormality in the wafer being processed this time.

[0028] Moreover, the information processing device 1 can visualize the parameters of the model obtained by performing dynamic mode decomposition, for example, by graphing and displaying them, and provide them to the user. The parameters obtained by performing dynamic mode decomposition represent the characteristics (modes) of the data to be processed. The information processing device 1 of the present embodiment can perform visualization based on the obtained parameters, for example, by creating and displaying a graph representing the characteristics of the mode, and, for example, by creating and displaying a heat map representing the relationship between the mode and the original data in a matrix form.

[0029] <Device Configuration>

[0030] Figure 2 is a block diagram showing a configuration example of the information processing device 1 of the present embodiment. The information processing device 1 of the present embodiment is configured to include a processing unit 11, a storage unit 12, a communication unit 13, a display unit 14, an operation unit 15, and the like. Further, in the present embodiment, it is assumed that the processing is performed by one information processing device 1 for the sake of explanation, but the processing of the information processing device 1 may also be distributed among multiple devices.

[0031] The processing unit 11 is constituted by an arithmetic processing device such as a CPU (Central Processing Unit), an MPU (Micro-Processing Unit), a GPU (Graphics Processing Unit), or a quantum processor, a ROM (Read Only Memory), a RAM (Random Access Memory), and the like. The processing unit 11 performs various processes such as a process of controlling the operation of the substrate processing apparatus 3 and a process of detecting an abnormality of the substrate processing apparatus 3 by reading and executing the program 12a stored in the storage unit 12.

[0032] The storage unit 12 is constituted by a large-capacity storage device such as a hard disk, for example. The storage unit 12 stores various programs executed by the processing unit 11 and various data required for the processing of the processing unit 11. In the present embodiment, the storage unit 12 stores the program 12a executed by the processing unit 11. In addition, in the storage unit 12, a process DB12b for storing and accumulating control input data and observation temperature data and a model information storage unit 12c for storing parameters of a model generated by a process of dynamic mode decomposition using these data are provided.

[0033] In the present embodiment, the program (computer program, program product) 12a is provided in the form of being recorded on a recording medium 99 such as a memory card or an optical disc, and the information processing apparatus 1 reads the program 12a from the recording medium 99 and stores it in the storage unit 12. Among them, the program 12a may also be written in the storage unit 12 at the manufacturing stage of the information processing apparatus 1, for example. In addition, for example, the program 12a may be a program distributed by a remote server device or the like obtained by the information processing apparatus 1 through communication. For example, the program 12a may be read by a writing device from the program recorded on the recording medium 99 and written into the storage unit 12 of the information processing apparatus 1. The program 12a may be provided in the form of distribution via a network or in the form of being recorded on the recording medium 99.

[0034] The process DB12b of the storage unit 12 is a database that stores and accumulates data obtained by sampling and acquiring control input data to the substrate processing apparatus 3 and observation temperature data from the substrate processing apparatus 3 by the information processing apparatus 1. The process DB12b stores the control input data and the observation temperature data in correspondence with various information such as the acquisition time of the data and the identification information of the wafer to be processed. In addition, the process DB12b may store, for example, a determination result of normal / abnormal (qualified / unqualified) determined by measuring the characteristics of the wafer after the processing of the substrate processing apparatus 3 is completed.

[0035] The model information storage unit 12c stores information such as the parameters of the model obtained by performing dynamic mode decomposition on the control input data and the observed temperature data stored in the process DB 12b using the information processing device 1. In the present embodiment, the information processing device 1 performs dynamic mode decomposition processing using the obtained control input data and observed temperature data for each wafer processed by the substrate processing device 3 to generate a model, and stores the parameters of the generated model in the model information storage unit 12c. The model information storage unit 12c can establish a correspondence relationship between various information such as the parameters of the model generated by dynamic mode decomposition, the time of storing the information, and the identification information of the wafer to be processed, and store them. In addition, the model information storage unit 12c can store information such as the result of abnormality determination based on the parameters of the model, for example.

[0036] The communication unit 13 is connected to the substrate processing device 3 via a cable such as a communication line or a signal line, and data is transmitted and received between the communication unit 13 and the substrate processing device 3 via the cable. In the present embodiment, the communication unit 13 transmits the control input data provided by the processing unit 11 to the substrate processing device 3. Further, the communication unit 13 receives the observed temperature data transmitted from the substrate processing device 3, and provides the received observed temperature data to the processing unit 11.

[0037] The display unit 14 is configured using a liquid crystal display or the like, and displays various images, characters, etc. based on the processing of the processing unit 11. In the present embodiment, the display unit 14 displays various information related to the operation state of the substrate processing device 3, for example, and also displays various information obtained by dynamic mode decomposition.

[0038] The operation unit 15 accepts the operation of the user and notifies the processing unit 11 of the accepted operation. For example, the operation unit 15 accepts the operation of the user through an input device such as a mechanical button or a touch panel provided on the surface of the display unit 14. In addition, for example, the operation unit 15 can be an input device such as a mouse and a keyboard, and these input devices can also be configured to be removable from the information processing device 1.

[0039] In addition, the storage unit 12 can be an external storage device connected to the information processing device 1. Further, the information processing device 1 can also be a multi-computer composed of multiple computers, or can also be a virtual machine virtually constructed by software. In addition, the information processing device 1 is not limited to the above configuration. For example, it may not include the display unit 14 and the operation unit 15, etc.

[0040] In addition, in the information processing device 1 of the present embodiment, the program 12a stored in the storage unit 12 is read out and executed by the processing unit 11, thereby controlling the processing unit 11a, the data acquisition unit 11b, the dynamic mode decomposition processing unit 11c, the abnormality determination unit 11d, the display processing unit 11e, etc. to be implemented as software functional units by the processing unit 11.

[0041] The control processing unit 11a controls the operation of the substrate processing apparatus 3 by generating control input data according to a predetermined semiconductor manufacturing process and sending it to the substrate processing apparatus 3. For example, the control processing unit 11a provides data such as the temperature increase or decrease amount or the operation amount of the device to one or more temperature control devices such as heaters and coolers provided in the substrate processing apparatus 3 as control input data. Thereby, the information processing apparatus 1 can control the temperature of the wafer processed by the substrate processing apparatus 3.

[0042] The data acquisition unit 11b acquires the control input data input by the control processing unit 11a to the substrate processing apparatus 3 and the observed temperature data measured by one or more temperature sensors provided in the substrate processing apparatus 3. The data acquisition unit 11b samples and acquires these data at a predetermined cycle such as once per second or once per minute. The data acquisition unit 11b stores the acquired control input data, observed temperature data, the acquisition time of the data, and the identification information of the wafer to be processed in association with the process DB 12b. By acquiring data at a predetermined cycle and storing it in the process DB 12b by the data acquisition unit 11b, time-series data of the control input data and the observed temperature data is accumulated in the process DB 12b.

[0043] The dynamic mode decomposition processing unit 11c performs dynamic mode decomposition based on the time-series control input data and observed temperature data acquired and stored in the process DB 12b by the data acquisition unit 11b. After the processing of one wafer by the substrate processing apparatus 3 is completed, for example, the dynamic mode decomposition processing unit 11c reads out the time-series control input data and observed temperature data acquired and stored during the processing of the wafer from the process DB 12b. The dynamic mode decomposition processing unit 11c performs dynamic mode decomposition based on the read time-series data. In addition, the dynamic mode decomposition processing unit 11c can perform either dynamic mode decomposition using only the observed temperature data or dynamic mode decomposition with control input using the control input data and the observed temperature data. Which dynamic mode decomposition the dynamic mode decomposition processing unit 11c performs can be determined by the user's selection, for example. The dynamic mode decomposition processing unit 11c stores the parameters of the model obtained by the dynamic mode decomposition processing in the model information storage unit 12c.

[0044] The abnormality determination unit 11d performs the following processing: Based on the parameters of the model obtained by dynamic mode decomposition, it determines whether an abnormality occurs when the substrate processing apparatus 3 processes a wafer corresponding to the time series data used for dynamic mode decomposition. In the present embodiment, time series data (control input data and observed temperature data) are collected in advance for the case where the processing of the wafer is performed normally and the case where an abnormality occurs. Moreover, for each wafer processed, dynamic mode decomposition of the time series data is performed, and the process of obtaining the parameters of the model is performed in advance. Based on the parameters in the normal state and the parameters in the abnormal state obtained in advance, a threshold value for distinguishing between normal and abnormal parameters is determined in advance, and the threshold value is stored in the storage unit 12 of the information processing apparatus 1 as a determination condition. The abnormality determination unit 11d determines the presence or absence of an abnormality in the current processing of the wafer by comparing the parameters obtained by the dynamic mode decomposition by the dynamic mode decomposition processing unit 11c with the threshold value determined in advance.

[0045] In addition, the parameters obtained by dynamic mode decomposition are a vector or a matrix including a plurality of values. For example, threshold values for determining abnormalities are respectively specified for each component of the vector or the matrix. The abnormality determination unit 11d can determine that there is an abnormality in the processing of the wafer when at least one of the components of the parameters is determined to be abnormal by comparison with the threshold value. And, for example, a threshold value can also be set for the sum value or the average value, etc. of the plurality of values included in the parameters. And, for example, values representing the parameters such as the singular value or the eigenvalue of the parameters can also be used for abnormality determination. And, for example, data in which a positive solution flag indicating the presence or absence of an abnormality is associated with the parameters calculated by dynamic mode decomposition based on the time series data collected in advance can be used as learning data. By performing so-called supervised machine learning using this learning data, an abnormality determination model for the presence or absence of input / output abnormalities of the parameters can be generated. The abnormality determination unit 11d can also perform determination using such an abnormality determination model.

[0046] The display processing unit 11e performs processing of displaying various information related to the control processing of the control processing unit 11a, information related to the result of the abnormality determination of the abnormality determination unit 11d, and other various information on the display unit 14. And, in the present embodiment, the display processing unit 11e performs processing of visualizing and displaying the parameters of the model obtained by the dynamic mode decomposition processing of the dynamic mode decomposition processing unit 11c on the display unit 14. The display processing unit 11e can display, for example, a chart representing the characteristics of the patterns included in the parameters of the model on the display unit 14. The display processing unit 11e can display, for example, a heat map representing the relationship between the patterns and the original time series data in a matrix form on the display unit 14. In addition, the display processing unit 11e can also perform any other display other than these.

[0047] <Dynamic Mode Decomposition>

[0048] The dynamic mode decomposition will be briefly described below. The model generated in the dynamic mode decomposition with control input is represented by the following equation (1). In this equation (1), X is a vector of observed temperature data, and Υ is a vector of control input data. Also, in equation (1), A and B are matrices and are parameters calculated by the dynamic mode decomposition.

[0049] [Equation 1]

[0050] XD π = AX + Bγ…(1)

[0051] Also, the left side of equation (1) represents the term obtained by performing some transformation D π on the observed temperature data X. Here, it is assumed that the first-order differential D (1) represented by the following equation (2) is used as the transformation D π , and the case where matrix B is 0. Among them, D π shown in equation (2) is an example and is not limited to this.

[0052] [Equation 2]

[0053]

[0054] Thus, the above equation (1) can be transformed into the following equation (3).

[0055] [Equation 3]

[0056] XD (1) = AX…(3)

[0057] Here, if the observed temperature data X = [x 0 , x 1 , …, x T , then the above equation (3) becomes an equation in the form of the following equation (4). In addition, x t is a vector of dimensions equal to the number of sensors provided in the substrate processing apparatus 3, where (t = 0, 1, …, T).

[0058] [Equation 4]

[0059] x t+1 = Ax t …(4)

[0060] Also, if X 0:T = [x 0 , x 1 , …, x T-1 , X 1:T+1 = [x 1 , x 2 , …, xT , then the above formula (4) becomes the following formula (5).

[0061] [Equation 5]

[0062] X 1:T+1 = AX 0:T …(5)

[0063] In dynamic mode decomposition, by using two matrices X made based on the observed temperature data X 0:T and X 1:T+1 to calculate the matrix A that satisfies formula (5), the parameters of the model can be calculated.

[0064] In addition, in this embodiment, a method for calculating the matrix A as a parameter in the case where B = 0 in formula (1), that is, in the case of general (uncontrolled input) dynamic mode decomposition, is described. In the case where B ≠ 0, that is, in the case of dynamic mode decomposition with control input, the method for calculating the parameters A and B is omitted from the detailed description, but the parameters A and B can be calculated by the same method.

[0065] In addition, the calculation of the parameters based on the above operation formula is an example of dynamic mode decomposition (DMD (Dynamic Mode Decomposition)), and is not limited thereto. There are various variations of dynamic mode decomposition such as Hankel DMD, resDMD, optDMD (Optimized DMD), and BOP-DMD (Bagging-Optimized DMD). The information processing device 1 can use these various dynamic mode decomposition methods to calculate the parameters. Hankle DMD is a method of dynamic mode decomposition that improves the acquisition of historical effects and the inference of parameters by using a vector formed by combining values of multiple time steps as the state vector. resDMD is a method of dynamic mode decomposition that uses the reference term of ResNet (Residual Neural Networks). optDMD is a method of dynamic mode decomposition that improves the modeling accuracy using a non-linear optimization framework to solve the deviation caused by data noise. BOP-DMD is a method of dynamic mode decomposition that improves the robustness by performing an operation of randomly extracting snapshots of time series data to form a subset and applying optDMD to the subset for integration.

[0066] In the method for dynamic mode decomposition of the information processing system according to the present embodiment, it is not limited to short-term prediction, and can perform prediction for medium- and long-term intervals, and can perform optimization of parameters based on the prediction results, etc. When the control equation (for example, the above formula (1)) has a simple structure, medium- and long-term prediction can be performed with higher accuracy. For example, predicting the temperature change in the semiconductor surface treatment process from the start to the end of the process, and the optimal parameters can be determined from multiple parameter candidates based on the evaluation index determined by the user. The parameters here include parameters for correcting equipment differences such as heaters or temperature sensors.

[0067] Figure 3 FIG. 4 is a flowchart showing an example of the process of the abnormality determination process performed by the information processing apparatus 1 according to the present embodiment. The control processing unit 11a of the processing unit 11 of the information processing apparatus 1 according to the present embodiment starts substrate processing such as etching of a wafer by accepting an operation for starting processing by a user, for example (step S1).

[0068] The data acquisition unit 11b of the processing unit 11 acquires the control input data input to the substrate processing apparatus 3 and the observed temperature data observed by the sensor of the substrate processing apparatus 3 (step S2). The data acquisition unit 11b stores the control input data and the observed temperature data acquired in step S2 in association with information such as the acquisition time of the data and the identification information of the wafer to be processed in the process DB 12b (step S3).

[0069] The data acquisition unit 11b determines whether the substrate processing for the wafer has ended (step S4). If the substrate processing has not ended (S4: No), the data acquisition unit 11b returns the process to step S2 and repeats the acquisition and storage of data.

[0070] If the substrate processing has ended (S4: Yes), the data acquisition unit 11b reads out and acquires the time-series control input data and observed temperature data stored in the process DB 12b during the period from the beginning to the end of the substrate processing related to the wafer (step S5).

[0071] The dynamic mode decomposition processing unit 11c of the processing unit 11 performs a dynamic mode decomposition process based on the time-series control input data and observed temperature data acquired in step S6 (step S6). In addition, at this time, the dynamic mode decomposition processing unit 11c may perform a dynamic mode decomposition process with control input using both the control input data and the observed temperature data, or may perform a dynamic mode decomposition process without control input using only the observed temperature data. Which process the dynamic mode decomposition processing unit 11c performs can be determined based on the user's selection, for example.

[0072] The abnormality determination unit 11d of the processing unit 11 compares the parameters of the model with a predetermined threshold value (step S7). The model receives, as input, time series data at a certain time obtained by performing the dynamic mode decomposition process in step S6, and predicts the time series data at the next time. The abnormality determination unit 11d determines the presence or absence of an abnormality in the substrate processing performed this time based on the comparison between the parameters of the model (the matrices A and B in the above formula (1), or only matrix A) and the threshold value (step S8). In the case of an abnormality (S8: Yes), the display processing unit 11e of the processing unit 11 notifies the user of the abnormality by displaying a message indicating the detected abnormality on the display unit 14 (step S9), and ends the process. In the case of no abnormality (S8: No), the processing unit 11 ends the process.

[0073] <Information display>

[0074] In the dynamic mode decomposition performed by the information processing apparatus 1 of the present embodiment, it is possible to calculate the parameters of the model based on the time series data as described above, and perform dimensionality reduction of the time series data. By performing dimensionality reduction based on dynamic mode decomposition using the information processing apparatus 1, reduced-dimensional data (modes) representing the characteristics of the original time series data and a matrix representing the correspondence between the reduced-dimensional data and the original time series data are obtained. Hereinafter, in the present embodiment, this reduced-dimensional data is regarded as data approximately representing the internal state of the substrate processing apparatus 3, and is referred to as "internal state data".

[0075] The observed temperature data X of the time series used in the above formula (5) 0:T =[x 0 , x 1 , …, x T-1 can be decomposed into three matrices shown in the following formula (6) by performing singular value decomposition. In formula (6), Σ is a matrix of singular values, U is a unitary matrix, and V* is the adjoint matrix of the unitary matrix V.

[0076] [Equation 6]

[0077] X 0:T =U∑V * …(6)

[0078] In this formula (6), ΣV * corresponds to the above internal state data, and U corresponds to a matrix representing the relationship between the observed temperature data and the internal state data. In addition, the correspondence between these matrices and the parameter A shown in the above formula (5) is represented by the following formula (7).

[0079] [Equation 7]

[0080] A = X 1：T+1 V∑ -1 U* …(7)

[0081] Figure 4 is a graph showing an example of observed temperature data representing a time series. In this example, it is assumed that the substrate processing apparatus 3 is equipped with six sensors for temperature measurement. The illustrated graph has the horizontal axis as time t and the vertical axis as the observed temperatures measured by six sensors 0 to 5. The information processing apparatus 1 can create the illustrated graph based on the observed temperature data periodically acquired from the substrate processing apparatus 3 and stored in the process DB 12b, and display it on the display unit 14. In addition, this graph corresponds to the graph obtained by graphing X in Equation (6). 0:T The graph obtained by graphing.

[0082] Figure 5 is a graph showing an example of internal state data obtained by dynamic mode decomposition. The illustrated graph has the horizontal axis as time t and the vertical axis as a value representing the internal state of the substrate processing apparatus 3. Figure 5 The internal state data shown is based on Figure 4 the observed temperature data shown, and is data obtained by performing dynamic mode decomposition processing. In this example, six observed temperature data are reduced to three internal state data.

[0083] The information processing apparatus 1 can perform dynamic mode decomposition processing based on the observed temperature data periodically acquired from the substrate processing apparatus 3 and stored in the process DB 12b, and obtain the reduced internal state data. The information processing apparatus 1 can create the illustrated graph based on this internal state data and display it on the display unit 14. In addition, this graph corresponds to the graph obtained by graphing ΣV in Equation (6). * The graph obtained by graphing.

[0084] If the matrix U of the above Equation (6) is used, the relationship between the temperature observation data x t and the internal state data y t is represented by the following Equation (8).

[0085] [Equation 8]

[0086] y t = U * x t …(8)

[0087] If, based on this Equation (8), an equation representing the time evolution of the internal state of the substrate processing apparatus 3 is obtained, it is the following Equation (9).

[0088] [Equation 9]

[0089] y t+1 = U * X 1：T+1 VΣ -1 yt …(9)

[0090] By using the matrix U*X included in the formula (9) 1:T+1 VΣ -1 , the information processing device 1 can create Figure 5 the chart shown

[0091] Figure 6 is a heat map showing an example of the matrix U obtained by dynamic mode decomposition. In this example, it is represented by blocks arranged in a 6×3 matrix Figure 4 the correspondence between the six observed temperature data shown Figure 5 and the three internal state data shown. The heat map shows the observed temperature data of six sensors 0 to 5 vertically and the three internal state data horizontally, indicating the relationship (correlation) between the observed temperature data and the internal state data corresponding to the color of the blocks at the intersections of the vertical and horizontal directions

[0092] In the case of this example, the information processing device 1 can calculate the matrix U of size 6×3 by dynamic mode decomposition. The information processing device 1 can create Figure 6 the heat map shown by coloring the inside of the blocks arranged in a 6×3 matrix with the types and shades of colors corresponding to the values of the respective elements included in the matrix U. The information processing device 1 can determine the type of color according to whether the value of the matrix U corresponding to each block is positive or negative, and determine the shade of color according to the magnitude of the absolute value of the value. The information processing device 1 can create a heat map based on the matrix U obtained by dynamic mode decomposition and display it on the display unit 14. In addition, in Figure 6 , hatching is marked in each block of the heat map, and the direction of the hatching indicates the type of color, and the density of the hatching indicates the shade of color

[0093] In the illustrated heat map, for example, the observed temperature data of sensor 0 has a large correlation with internal states 0 and 1 in the negative direction and a large correlation with internal state 2 in the positive direction. And, for example, the observed temperature data of sensor 5 has a large correlation with internal state 0 in the positive direction and almost no correlation with internal states 1 and 2

[0094] And Figure 4 each chart of the observed temperature data shown can be based on Figure 5 the chart of the internal state data shown and Figure 6Approximate generation of the heat map shown. For example, the graph of the observed temperature data of sensor 0 is equivalent to the graph obtained by multiplying the value of the block corresponding to sensor 0 of the heat map and internal state 0 by the graph of internal state 0, the graph obtained by multiplying the value of the block corresponding to sensor 0 of the heat map and internal state 1 by the graph of internal state 1, and the graph obtained by multiplying the value of the block corresponding to sensor 0 of the heat map and internal state 2 by the graph of internal state 2, and then adding them together. The graphs of the observed temperature data of other sensors are the same.

[0095] By comparing, for example, the graph and heat map obtained by performing dynamic mode decomposition on the observed data during the processing of wafers judged to be normal with the graph and heat map obtained by performing dynamic mode decomposition on the observed data during the processing of wafers judged to be abnormal, the user can expect to infer the cause of the abnormality, etc.

[0096] Similarly, the information processing device 1 can perform the following processing: pre-store graphs and heat maps made based on the observed data during the processing of wafers judged to be normal or abnormal in the past, and infer the cause of the abnormality, etc. based on the difference from the graphs and heat maps made this time. In addition, instead of making and comparing the graphs and heat maps, the information processing device 1 can compare the information used to make these graphs and heat maps, that is, the internal state data and the matrix representing the relationship between the observed temperature data and the internal state data, etc.

[0097] Regarding, for example Figure 5 For the graph of the internal state data shown, when there is a difference between the graph in the normal state and the graph in the abnormal state, the user or the information processing device 1 can infer that there is a cause of abnormality in the internal state of the substrate processing device 3, etc. And regarding, for example Figure 6 For the heat map shown, when there is a difference between the heat map in the normal state and the heat map in the abnormal state, the user or the information processing device 1 can infer that the abnormality is due to sensor - specific reasons.

[0098] In addition, in this example, the method of displaying the graph and heat map in the case where B = 0 in equation (1), that is, in the case of general (uncontrolled - input) dynamic mode decomposition, has been described. Although the detailed description is omitted, in the case where B ≠ 0, that is, in the case of dynamic mode decomposition with control input, it is the same, and the display of the graph and heat map can be performed.

[0099] Figure 7It is a flowchart showing an example of the process of information display processing performed by the information processing apparatus 1 of the present embodiment. The processing unit 11 of the information processing apparatus 1 of the present embodiment starts the information display processing, for example, by accepting an instruction from the user for information display (step S21). The data acquisition unit 11b of the processing unit 11 reads and acquires the time-series control input data and observed temperature data stored in the process DB 12b during the period from the beginning to the end of the substrate processing related to the wafer to be displayed (step S22).

[0100] The dynamic mode decomposition processing unit 11c of the processing unit 11 performs dynamic mode decomposition processing based on the time-series control input data and observed temperature data acquired in step S22 (step S23). In addition, at this time, the dynamic mode decomposition processing unit 11c may perform dynamic mode decomposition with control input using both the control input data and the observed temperature data, or may perform dynamic mode decomposition without control input using only the observed temperature data. Which processing the dynamic mode decomposition processing unit 11c performs can be determined based on, for example, the user's selection.

[0101] The display processing unit 11e of the processing unit 11 creates a chart of the time-series observed temperature data acquired in step S22, for example (step S24). And the display processing unit 11e creates a chart of the internal state data (data obtained by reducing the dimensionality of the observed temperature data) of the substrate processing apparatus 3 obtained by the dynamic mode decomposition processing in step S23 (step S25). And the display processing unit 11e creates a heat map of the matrix U representing the relationship between the observed temperature data and the internal state data obtained by the dynamic mode decomposition processing in step S23 (step S26). The display processing unit 11e displays the charts created in steps S24 and S25 and the heat map created in step S26 on the display unit 14 (step S27), and ends the processing.

[0102] <Modification Example>

[0103] In the above embodiment, the temperature control of the substrate processing apparatus 3 is taken as an example for explanation, but the application of the present technology is not limited to temperature control. Figure 8 It is a schematic diagram for explaining the outline of the information processing system of the modification example. The information processing system of the modification example is a system for performing abnormality determination or the like on the substrate processing apparatus 3 that transports wafers, for example.

[0104] The substrate processing apparatus 3 of the modification example has a transfer mechanism for transferring wafers. A movable part 3b that moves according to the operation of an actuator or a motor or the like is provided in the transfer mechanism. The substrate processing apparatus 3 drives an actuator or a motor or the like according to the control input data from the information processing apparatus 1, and the movable part 3b moves accordingly to transfer the wafer.

[0105] Further, the substrate processing apparatus 3 includes a sensor for measuring a position or the like. The information processing apparatus 1 acquires, at a prescribed cycle, the measurement result of the position of the movable part 3b by the sensor of the substrate processing apparatus 3 as observation position data. In addition, in this modified example, it is assumed that the measurement sensor measures the position of the movable part 3b, but it is not limited thereto, and the sensor may measure, for example, the speed or acceleration of the movable part 3b or the like. Further, when the movable part 3b rotates, for example, the rotational speed or angular velocity may be measured by the sensor. Further, the information processing apparatus 1 may acquire image data of the movable part 3b captured by a camera instead of the sensor. Further, the information processing apparatus 1 may acquire information obtained by combining these multiple pieces of information.

[0106] The information processing apparatus 1 acquires control input data and observation position data at a prescribed cycle and stores them in the process DB 12b. After the substrate processing apparatus 3 finishes transporting the wafer, the information processing apparatus 1 can perform dynamic mode decomposition based on the time-series control input data and observation position data stored in the process DB 12b.

[0107] Furthermore, the application of the present technology is not limited to temperature control and wafer transfer control. The present technology can be applied to control directly or indirectly related to the state of the substrate processing apparatus 3.

[0108] <Modified Example 2>

[0109] In the above-described embodiment, the information processing apparatus 1 acquires control input data and observation temperature data by sampling the input / output signals to the substrate processing apparatus 3 at a prescribed cycle. However, the acquisition of control input data, observation temperature data, etc. is not limited to periodic sampling.

[0110] Figure 9 is a schematic diagram for explaining a method for acquiring control input data and observation temperature data of the information processing apparatus 1 in Modified Example 2. In the information processing system of Modified Example 2, the information processing apparatus 1 inputs Figure 9 a pulse-like signal as shown in the upper part as control input data to the substrate processing apparatus 3. This control input data controls, for example, the timing of applying laser or heat in a pulsed manner during surface processing of the substrate, and the substrate processing apparatus 3 performs processing such as laser based on the input of a high-level signal. And the control input data in this example is a signal that non-periodically repeats changes between high level and low level.

[0111] In this example, the information processing device 1 needs to obtain the observed data such as temperature observed by sensors and the like when the substrate processing device 3 performs processing such as laser processing, and does not need the observed data in the case where no processing is performed. The information processing device 1 of Modification 2 obtains the observed temperature data in the case where the control input data is in a specified state, and in this example, in the case of high level. Figure 9 The control input data shown includes the periods during which the five signals (1) to (5) are at high level. The information processing device 1 can obtain five values (1) to (5) by performing the acquisition of the observed temperature data during each high level period, and processes the obtained values in order as time series observed temperature data.

[0112] In addition, during each high level period, the information processing device 1 can also perform data acquisition multiple times, and uses a representative value such as the average value or the median value of the calculated multiple values as the observed temperature data for one quantity. Also, the information processing device 1 can perform data acquisition multiple times during each period when the control input data becomes high level, and independently use these data as time series observed temperature data.

[0113] <Modification 3>

[0114] The information processing device 1 of the present embodiment repeatedly obtains the control input data input to the substrate processing device 3 and the observed temperature data obtained by observing the substrate processing device 3, and performs a dynamic mode decomposition process based on these time series data to generate a prediction model. At this time, the information processing device 1 can perform various preprocessings on the time series data (control input data and / or observed temperature data) used for the dynamic mode decomposition. Hereinafter, some preprocessings that the information processing device 1 can perform will be described.

[0115] · Removing low-frequency interference

[0116] Regarding low-frequency interference such as offset or drift, low-frequency interference is generated due to various factors such as the operation at the equilibrium point and the temperature-dependent characteristics of the sensor, and may deteriorate the modeling accuracy. Therefore, the information processing device 1 can perform operations such as calculating the average value based on the obtained time series data, subtracting using the prior information related to the equilibrium point, or calculating the difference of the data as preprocessing to remove the low-frequency interference.

[0117] · Removing high-frequency interference

[0118] By removing the influence of noise that is not an object of modeling or the high-frequency domain dynamics included in the time series data, it is possible to expect an improvement in the SNR and an improvement in the modeling accuracy. The information processing device 1 can remove high-frequency interference by applying a filter that attenuates the high-frequency domain in the frequency domain, such as a low-pass filter or a moving average filter.

[0119] · Remove outliers or missing values

[0120] By pre - removing outliers such as outliers or missing values caused by sensor abnormalities, etc., or performing pre - processing such as interpolation from other time - series data through the information processing device 1, it is possible to expect an improvement in the accuracy of modeling.

[0121] · Interception of data

[0122] By the information processing device 1 only intercepting the time - series data in the interval required for modeling, it is possible to expect a reduction in unnecessary dynamics or noise and an improvement in the accuracy of modeling.

[0123] · Extraction

[0124] There is an appropriate value for the sampling period of the time - series data in order to improve the modeling accuracy according to the time constant of the system to be targeted. The information processing device 1 collects time - series data with as short a sampling period as possible and then performs pre - processing of extraction, so that it can process data with an appropriate sampling period. Extraction is a process of performing down - sampling and low - pass filtering. In the extraction process, aliasing may occur in which frequency components above the Nyquist frequency wrap around into the low - frequency range. Therefore, it is preferable to use an anti - aliasing filter, which is a low - pass filter with the Nyquist frequency as the cut - off frequency.

[0125] <Summary>

[0126] In the information processing system of the present embodiment configured as above, the information processing device 1 acquires time - series observed temperature data obtained by observing the temperature as the state of the substrate processing device 3, and calculates the parameters of the model for predicting the observation information at the second moment based on the observation information at the first moment through dynamic mode decomposition of the acquired observation data. In addition, the first and second observation information may be the observation data itself or data obtained by performing some arithmetic processing on the observation data. By calculating the parameters through dynamic mode decomposition based on the time - series data related to the substrate processing device 3, the information processing device 1 can expect to use the calculated parameters to determine the presence or absence of abnormalities related to the processing performed by the substrate processing device 3, and can expect to effectively utilize the time - series data obtained from the substrate processing device 3.

[0127] Also, in the information processing system of the present embodiment, the information processing device 1 acquires time-series control input data for the substrate processing device 3, and calculates the parameters of a model that predicts the second observation information at the second moment based on the first control information and the first observation information at the first moment through dynamic mode decomposition including the control input, based on the acquired control input data and the observed temperature data. The control input information can be the control input data itself, or data obtained by performing certain arithmetic operations on the control input data. Thus, the information processing device 1 can perform dynamic mode decomposition using not only the observed temperature data but also the control input data to determine the presence or absence of anomalies, etc., so it is possible to expect to perform such determination processing with higher accuracy.

[0128] Also, in the information processing system of the present embodiment, for each processing unit of the substrate processing device 3, for example, for each processed wafer, the information processing device 1 calculates the parameters of the model based on dynamic mode decomposition. By comparing the parameters calculated for each processing unit with, for example, the parameters related to wafers that have been processed normally, and the parameters related to wafers for which anomalies have been detected, etc., it is possible to expect to determine the presence or absence of anomalies.

[0129] Also, in the information processing system of the present embodiment, the information processing device 1 obtains the internal state data (modes) of the substrate processing device 3 and a matrix representing the relationship between the observed temperature data and the internal state data through dynamic mode decomposition. The information processing device 1, for example, compares the past normal / anomalous modes with the current mode to detect differences related to the internal state of the substrate processing device 3, and can expect to infer the cause of anomalies related to the current substrate processing, etc. Also, the information processing device 1 compares, for example, the past normal / anomalous relationship matrices with the current relationship matrix to detect differences related to the observation system such as sensors of the substrate processing device 3, and can expect to infer the cause of anomalies related to the current substrate processing, etc.

[0130] Also, in the information processing system of the present embodiment, the internal state data (modes) of the substrate processing device 3 and the matrix representing the relationship between the observed temperature data and the internal state data are visualized as a chart or a heat map, etc., and displayed. Thus, the user can expect to infer the cause of anomalies related to the substrate processing based on the displayed chart or heat map, etc.

[0131] Also, in the information processing system of the present embodiment, data related to the heating or cooling of the wafers processed by the substrate processing device 3 is used as the control input data, and data related to the temperature of the wafers measured by the sensors is used as the observation data. Thus, the information processing device 1 can expect to perform determination of anomalies related to the temperature control of the substrate processing device 3, etc.

[0132] Further, in the information processing system of the present embodiment, the data input for controlling the movable part 3b of the substrate processing apparatus 3 is used as control input data, and the data related to the position, speed, or acceleration of the movable part 3b measured by the sensor is used as observation data. Thus, the information processing apparatus 1 can expect to perform determination of abnormalities related to the control of the movable part 3b such as a wafer transfer mechanism provided in the substrate processing apparatus 3.

[0133] In addition, in the present embodiment, the temperature control of the substrate processing apparatus 3 and the control of the movable part 3b are taken as examples for explanation. However, the application of the present technology is not limited to these two controls and can be applied to various controls of the substrate processing apparatus 3.

[0134] Moreover, the charts, heat maps, etc. illustrated in the present embodiment are only examples and are not limited thereto. In addition, the information processing apparatus 1 can also visualize and display various information obtained by dynamic mode decomposition in any manner.

[0135] The embodiments disclosed this time are illustrative in all respects and should not be considered restrictive. The scope of the present disclosure is not represented by the above description but by the claims, and is intended to include all modifications within the meaning and scope equivalent to the claims.

[0136] The matters described in each embodiment can be combined with each other. In addition, the independent claims and dependent claims described in the claims can be combined with each other in all combinations regardless of the citation form. Moreover, the claims use the form of a claim that cites two or more other claims (multiple dependent claim form), but are not limited thereto, and can also be described in the form of a multiple dependent claim (multiple citation multiple dependent claim) that cites at least one multiple dependent claim.

[0137] Description of Reference Numerals

[0138] 1 Information processing apparatus (computer); 3 Substrate processing apparatus; 3a Electrostatic chuck; 3b Movable part; 11 Processing unit; 11a Control processing unit; 11b Data acquisition unit (acquisition unit); 11c Dynamic mode decomposition processing unit (calculation unit); 11d Abnormality determination unit; 11e Display processing unit; 12 Storage unit; 12a Program (computer program); 12b Process DB; 12c Model information storage unit; 13 Communication unit; 14 Display unit; 15 Operation unit.

Claims

1. An information processing method, wherein, the following processing is performed by an information processing device: obtaining time - series observation data obtained by observing the state of a substrate processing device; and calculating parameters of a model based on the obtained time - series observation data through dynamic mode decomposition, where the model is a model for predicting second observation information related to observation data at a second moment after the first moment based on first observation information related to the observation data at the first moment.

2. The information processing method according to claim 1, wherein, obtaining time - series control input data for the substrate processing device, calculating the parameters of the model through dynamic mode decomposition with control input based on the obtained time - series control data and the time - series observation data, where the model is a model for predicting the second observation information based on first control information related to the control input data at the first moment and the first observation information.

3. The information processing method according to claim 1, wherein, calculating the parameters of the model for each processing unit of the substrate processing device, comparing the parameters of each processing unit to detect differences in the state of the substrate processing device between the processing units.

4. The information processing method according to claim 3, wherein, through the dynamic mode decomposition, obtaining a plurality of modes related to the state of the substrate processing device, comparing the modes of each processing unit to detect differences in the state of the substrate processing device between the processing units.

5. The information processing method according to claim 4, wherein, through the dynamic mode decomposition, obtaining relationship information between the plurality of modes and the observation data, comparing the relationship information of each processing unit to detect differences in the observation system of the substrate processing device between the processing units.

6. The information processing method according to claim 4, wherein, displaying a chart representing the characteristics of the mode and a heat map representing the relationship between the mode and the observation data in a matrix form.

7. The information processing method according to claim 2, wherein, the control input data is data of a control input related to heating or cooling of a wafer processed by the substrate processing device, the observation data is observation data related to the temperature of the wafer.

8. The information processing method according to claim 2, wherein, the control input data is data of a control input for a movable part of the substrate processing device, the observation data is observation data related to the position, speed, or acceleration of the movable part.

9. A computer program that causes a computer to perform the following processing: obtaining time - series observation data obtained by observing the state of a substrate processing device, calculating parameters of a model based on the obtained time - series observation data through dynamic mode decomposition, where the model is a model for predicting second observation information related to observation data at a second moment after the first moment based on first observation information related to the observation data at the first moment.

10. An information processing device, comprising: An acquisition unit that acquires time-series observation data obtained by observing the state of a substrate processing apparatus; and A calculation unit that calculates parameters of a model based on the acquired time-series observation data by performing dynamic mode decomposition, the model being a model that predicts second observation information related to observation data at a second time after the first time based on first observation information related to observation data at the first time.

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