Information processing method, computer program, and information processing device

Abstract

The invention provides an information processing method, a computer program, and an information processing device which are expected to effectively utilize data obtained from a target device. According to the information processing method of the embodiment, the information processing device acquires time series observation data related to a target device, calculates a first parameter and a second parameter of a model through dynamic mode decomposition based on the acquired observation data, and performs the following processing. The model is a model for predicting time evolution data of observation data on the basis of the observation data, the first parameter is a parameter relating to a conversion function for converting the observation data into the time evolution data, and the second parameter is a parameter relating to a function for interpreting the observation data of the time evolution data.

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, which acquires data related to industrial machinery, based on the acquired data related to industrial machinery, creates 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 an object device.

[0005] An information processing method according to an embodiment is processed by an information processing apparatus as follows: acquiring time series observation data related to an object device, calculating a first parameter and a second parameter of a model by dynamic mode decomposition based on the acquired observation data, the model being a model for predicting time evolution data of the observation data based on the observation data, the first parameter being a parameter related to a conversion function for converting the observation data into the time evolution data, and the second parameter being a parameter related to a function for explaining the observation data of the time evolution data.

[0006] Advantageous Effects of the Invention

[0007] According to the present disclosure, it is possible to expect effective utilization of data obtained from an object device. 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 the configuration of the information processing apparatus in the present embodiment.

[0010] Figure 3 It is a flowchart showing the process of parameter calculation processing performed by the information processing apparatus in the present embodiment.

[0011] Figure 4 It is a flowchart showing the process of abnormality determination processing performed by the information processing apparatus in the present embodiment.

[0012] Figure 5 It is a schematic diagram for explaining the outline of the information processing system of the modification example.

[0013] Figure 6 It is a flowchart showing the process of parameter calculation processing performed by the information processing apparatus of Modification 2. Detailed implementation mode

[0014] Hereinafter, specific examples of the information processing system according to the embodiment of the present disclosure will be described with reference to the drawings. Note that the present disclosure is not limited to these examples, and as indicated by the claims, it is intended to include all modifications within the meaning equivalent to the claims and within the scope.

[0015] <System outline>

[0016] 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 that performs processing such as etching on a semiconductor wafer. The substrate processing apparatus 3 has 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 in the figure), and a sensor for measuring the temperature of the wafer (not shown in the figure).

[0017] The information processing apparatus 1 is a device that controls and monitors the operation of the substrate processing apparatus 3, and controls the temperature of the substrate processing apparatus 3 in the present embodiment. 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.

[0018] 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. In addition, 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 the observed temperature data. Therefore, in the present embodiment, the control input data and the observed temperature data stored in the database of 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 one or both of the control input data and the observed temperature data may be one-dimensional scalar values.

[0019] 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 performed 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. In the present embodiment, the information processing apparatus 1 uses the method of "dynamic mode decomposition" to make such a determination of the presence or absence of an abnormality. Dynamic mode decomposition is a method of decomposing time series data into a plurality of variation factors (modes), and it is possible to generate a model for predicting 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 first-order differential value of the observed data at a subsequent 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 detailed description is omitted.

[0020] For example Figure 1In the example shown, the information processing device 1 performs "dynamic mode decomposition" processing based on the time-series observed temperature data obtained by the sensors of the substrate processing device 3. Thereby, 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 a subsequent moment or the data obtained by performing certain operations on the observed temperature data (hereinafter, these data are referred to as the time-evolution data of the observed temperature data). In the case of general dynamic mode decomposition, it is more common to use a model that accepts the observed temperature data as input and outputs the predicted value of the first-order differential value of the observed temperature data.

[0021] In the information processing system of the present embodiment, a model that accepts the observed temperature data as input and outputs the predicted value of the non-integer-order differential value represented by the non-integer-order differential equation as the time-evolution data is adopted as the above-mentioned model. The information processing device 1 of the present embodiment performs the following processing: taking the differential order of the non-integer-order differential equation and the parameters of the model calculated by the dynamic mode decomposition method together as parameters, and determining the differential order suitable under the given conditions.

[0022] Among them, the model generated by the information processing device 1 does not necessarily have a configuration that takes the observed temperature data acquired from the substrate processing device 3 as input and output. The model can also take, as input and output, data obtained by performing certain arithmetic processes (pre-processing) on the observed temperature data, such as the average value or differential value of the observed temperature data. For example, the model can have a configuration that accepts the average value of the observed temperature data within a specified time range at a certain moment and before that moment as input. In addition, for example, the model can have a configuration that accepts the first-order differential value of the observed temperature data at a certain moment as input. In addition, in the present embodiment, the time-evolution data output by the model is data represented by a non-integer-order differential equation, but the time-evolution data output by the model is not limited thereto.

[0023] Furthermore, in the present embodiment, the information processing device 1 uses the method of "dynamic mode decomposition with control input" that can append the time-series data of the processing control input in the dynamic mode decomposition. The information processing device 1 can generate, by using the method of dynamic mode decomposition with control input, 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 time-evolution data of the observed temperature data at a subsequent moment. In addition, since the method of dynamic mode decomposition with control input is a known analytical method (for example, refer to "Dynamic mode decomposition with control" by Joshua L. Proctor, Steven L. Brunton, J. Nathan Kutz, September 24, 2014), detailed description is omitted.

[0024] In this embodiment, the information processing device 1 performs a "dynamic mode decomposition with control input" process based on, for example, control input data for 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 accepts control input data and observed temperature data at a certain time as inputs and outputs predicted values of the time evolution data of the observed temperature data at a subsequent time. In addition, the control input data input to the model can be 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, in the same way as the model that outputs the predicted value of the observed temperature data. Further, in the following description, even when only "dynamic mode decomposition" is described, it includes this "dynamic mode decomposition with control input".

[0025] The information processing device 1 performs dynamic mode decomposition with control input based on the control input data and the observed temperature data acquired and stored in the database when the substrate processing device 3 processes one wafer. Thereby, the information processing device 1 can calculate the values of the internal parameters of the model that accepts control input data and observed temperature data at a certain time as inputs and outputs predicted values of the time evolution data of the observed temperature data at a subsequent time. For example, the time evolution data is data represented by a non-integer order differential equation, and the internal parameters of the model calculated by the information processing device 1 include the differential order of the non-integer order differential equation. The information processing device 1 compares the obtained model parameters with, for example, the model parameters determined using data collected for wafers that have been processed normally, or the model parameters 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.

[0026] <Device Configuration>

[0027] Figure 2 It is a block diagram showing the configuration of the information processing device 1 in this embodiment. The information processing device 1 in this 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 this embodiment, it is assumed that the processing of the information processing device 1 is performed by one information processing device 1 for explanation, but the processing of the information processing device 1 can also be distributed among multiple devices.

[0028] The processing unit 11 is composed of 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), and a RAM (Random Access Memory). The processing unit 11 performs various processes such as controlling the operation of the substrate processing apparatus 3 and detecting abnormalities in the substrate processing apparatus 3 by reading and executing the program 12a stored in the storage unit 12.

[0029] The storage unit 12 is composed of a large-capacity storage device such as a hard disk. 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. Further, in the storage unit 12, there are provided a process DB 12b for storing and accumulating control input data and observed temperature data, and a model information storage unit 12c for storing parameters of a model generated by processing using these data by dynamic mode decomposition.

[0030] In the present embodiment, the program (computer program, program product) 12a is provided in a form 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. Here, the program 12a may also be written in the storage unit 12 at the manufacturing stage of the information processing apparatus 1, for example. Further, for example, the program 12a may be obtained by the information processing apparatus 1 through communication of a program distributed from a remote server apparatus or the like. For example, the program 12a may be read by a writing device from a 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 a distributed form via a network or in a form recorded on the recording medium 99.

[0031] The process DB 12b of the storage unit 12 is a database for storing and accumulating data obtained by sampling and acquiring control input data to the substrate processing apparatus 3 and observed temperature data from the substrate processing apparatus 3 by the information processing apparatus 1. The process DB 12b stores the control input data and the observed temperature data in association with various information such as the acquisition time of the data and the identification information of the wafer to be processed. Further, the process DB 12b 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.

[0032] The model information storage unit 12c stores information such as the parameters of a 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 store by associating various information such as the parameters of the model generated by dynamic mode decomposition with the time of storing the information and the identification information of the wafer to be processed. In addition, the model information storage unit 12c can store information such as the result of anomaly determination based on the parameters of the model.

[0033] 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 performs data transmission and reception with the substrate processing device 3 via this cable. In the present embodiment, the communication unit 13 sends the control input data provided by the processing unit 11 to the substrate processing device 3. In addition, the communication unit 13 receives the observed temperature data sent from the substrate processing device 3, and provides the received observed temperature data to the processing unit 11.

[0034] 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.

[0035] The operation unit 15 accepts the user's operation and notifies the processing unit 11 of the accepted operation. For example, the operation unit 15 accepts the user's operation 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 input devices such as a mouse and a keyboard, and these input devices can also be configured to be removable from the information processing device 1.

[0036] In addition, the storage unit 12 can be an external storage device connected to the information processing device 1. And the information processing device 1 can be a multi-computer including a plurality of computers, or can be a virtual machine virtually constructed by software. And the information processing device 1 is not limited to the above configuration, and may not have, for example, the display unit 14 and the operation unit 15.

[0037] And in the information processing device 1 of the present embodiment, the processing unit 11 reads out the program 12a stored in the storage unit 12 and executes it, thereby controlling the processing unit 11a, the data acquisition unit 11b, the parameter calculation unit 11c, the anomaly determination unit 11d, the display processing unit 11e, etc. to be implemented as software functional units by the processing unit 11.

[0038] The control processing unit 11a performs the following processing: By generating control input data according to a pre-specified semiconductor manufacturing process and sending it to the substrate processing apparatus 3, etc., the operation of the substrate processing apparatus 3 is controlled. For example, the control processing unit 11a provides data such as the amount of increase or decrease in temperature or the operation amount of the apparatus 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.

[0039] The data acquisition unit 11b performs the following processing: It 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 specified 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 the data acquisition unit 11b acquiring data at a specified cycle and storing it in the process DB 12b, time-series data of the control input data and the observed temperature data is accumulated in the process DB 12b.

[0040] The parameter calculation unit 11c performs the following processing: It calculates the parameters of the model by performing a dynamic mode decomposition process based on the time-series control input data and observed temperature data acquired by the data acquisition unit 11b and stored in the process DB 12b. In the present embodiment, the model is a model that receives time-series observed temperature data (and control input data) as input and outputs the predicted value of the time evolution data of the observed temperature data. The time evolution data is, for example, data represented by a non-integer order differential equation, and the parameters calculated by the parameter calculation unit 11c include the differential order of the non-integer order differential equation. Hereinafter, the differential order of the non-integer order differential equation unique to the information processing system of the present embodiment is referred to as the first parameter, and the parameters calculated by the conventional dynamic mode decomposition are referred to as the second parameter. When only the parameter is described, it means including the first parameter and the second parameter. The parameter calculation unit 11c performs the processing of calculating the first parameter and the second parameter of the model based on the time-series control input data and observed temperature data stored in the process DB 12b.

[0041] In the present embodiment, for example, a user presets multiple values that are candidates for a first parameter (the order of differentiation of a non-integer order differential equation), and the parameter calculation unit 11c determines an optimal value from the set multiple candidate values. For example, the parameter calculation unit 1c selects one candidate value from the set multiple candidate values related to the first parameter to determine the order of differentiation of the non-integer order differential equation. Then, the parameter calculation unit 11c can calculate a second parameter of the model by performing dynamic mode decomposition based on the control input data and the observed temperature data stored in the process DB 12b. The parameter calculation unit 11c can perform dynamic mode decomposition on the non-integer order differential equation for all candidate values of the first parameter, and respectively calculate candidate values of the second parameter of the model corresponding to each candidate value. Thus, the parameter calculation unit 11c can obtain multiple sets of candidate values of the first parameter and the second parameter.

[0042] Next, the parameter calculation unit 11c inputs the time-series control input data and the observed temperature data stored in the process DB 12b into the model using the model with each candidate value of the first parameter and the second parameter set. The parameter calculation unit 11c obtains a predicted value of the time evolution data of the observed temperature data output by the model. In addition, the parameter calculation unit 11c calculates a differential value of the non-integer order differentiation as the true solution value of the time evolution data using the non-integer order differential equation with each candidate value of the first parameter set based on the time-series control input data and the observed temperature data stored in the process DB 12b. Then, the parameter calculation unit 11c calculates the error between the predicted value and the true solution value of the time evolution data. Thus, the parameter calculation unit 11c can calculate the error of the predicted value of the model for each candidate value of the first parameter, and can select the candidate value with the minimum error as the final first parameter.

[0043] After the substrate processing apparatus 3 finishes processing one wafer, for example, the parameter calculation unit 11c reads out the time-series control input data and the observed temperature data that are acquired and stored during the processing of the wafer from the process DB 12b. The parameter calculation unit 11c calculates the first parameter and the second parameter of the model based on the read time-series data. In addition, the parameter calculation 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 parameter calculation unit 11c performs can be determined by, for example, the user's selection. The parameter calculation unit 11c stores the calculated parameters of the model in the model information storage unit 12c.

[0044] The abnormality determination unit 11d performs the following processing: Based on the parameters of the model calculated by the parameter calculation unit 11c, it determines whether an abnormality occurs when the substrate processing apparatus 3 processes the wafer corresponding to the time series data used for dynamic mode decomposition. In the present embodiment, for the case where the processing of the wafer is normally performed and the case where an abnormality occurs, time series data (control input data and observed temperature data) are respectively collected in advance. For each wafer processing, 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 storage unit 12 of the information processing apparatus 1 stores the threshold value as a determination condition. The abnormality determination unit 11d determines whether there is an abnormality in the current wafer processing by comparing the parameters obtained by the dynamic mode decomposition by the parameter calculation unit 11c with the predetermined threshold value.

[0045] In addition, the parameters used for determination by the abnormality determination unit 11d can be both the first parameter and the second parameter, or either one of them. And the second parameter can be a vector or a matrix including a plurality of values. In the case where the parameter includes a plurality of values like this, for example, thresholds for determining abnormalities can be respectively specified for these plurality of values. When the abnormality determination unit 11d determines that there is an abnormality for at least one value by comparing it with the threshold value, it can determine that there is an abnormality in the processing of the wafer. Additionally, for example, a threshold value can be set for the sum value or the average value, etc. of the plurality of values included in the parameter. And, for example, data that establishes a correspondence between the positive solution flag indicating the presence or absence of an abnormality and the parameters calculated based on the time series data collected in advance can be used as learning data. The information processing apparatus 1 can generate an abnormality determination model for determining whether there is an abnormality in the input and output of the parameters by performing so-called supervised machine learning using the learning data. The abnormality determination unit 11d can also use this abnormality determination model for determination.

[0046] The display processing unit 11e performs processing of displaying various information related to the control processing of the control processing unit 11a, and various information such as information related to the result of the abnormality determination by the abnormality determination unit 11d on the display unit 14. In addition, in the present embodiment, when the abnormality determination unit 11d determines that there is an abnormality, the display processing unit 11e displays a message notifying the user of the main idea.

[0047] <Dynamic Mode Decomposition Incorporating Non-integer Order Differential Equation>

[0048] The information processing system according to the present embodiment calculates the parameters of the model by dynamic mode decomposition and determines whether there is an abnormality based on the time-series control input data and the observed temperature data obtained when processing the wafer in the substrate processing apparatus 3. The model generated by the conventional dynamic mode decomposition with control input is represented by, for example, the following equation (1).

[0049] [Equation 1]

[0050]

[0051] where x(t) included in the right side of Equation (1) is an element of the vector X = [x(t 0 ), x(t 1 ), …, x(t m-1 )] of the observed temperature data. u(t) is an element of the vector Υ = [u(t 0 ), u(t 1 ), …, u(t m-1 )] of the control input data. The left side of Equation (1) represents the first derivative value of the observed temperature data. The coefficients A and B are the parameters (second parameters) of the model and are calculated by dynamic mode decomposition. The model of Equation (1) can accept the observed temperature data and the control input data as inputs and output the predicted value of the first derivative value of the observed temperature data by determining the coefficients A and B.

[0052] In the conventional dynamic mode decomposition, as shown in the left side of Equation (1), a model that predicts the first derivative value of some time-series data is often used. However, the predicted value of the model may not be the first derivative value, as long as it is some value generated based on the present and past values of the time-series data. If Equation (1) is generalized based on this, it becomes the following Equation (2). In the present embodiment, Equation (2) is called the time evolution equation, and the model represented by the time evolution equation is called the time evolution model. In addition, the data represented by π(x)(t) on the left side of Equation (2) is called the time evolution data.

[0053] [Equation 2]

[0054] π(x)(t) = Ax(t) + Bu(t) … (2)

[0055] In this Equation (2), the transformation π represents a function that generates some value based on the observed temperature data x(t). Equation (1) is a formula in which the transformation π is taken as the first derivative d / dt. In the present embodiment, it is assumed that the transformation π is a linear transformation. That is, the result obtained by multiplying the observed temperature data at a specified time from the current to the past by the weight w and adding them becomes π(x)(t). If the matrix D π representing the weight is used to represent the transformation π, the above Equation (2) becomes the following Equation (3).

[0056] [Number 3]

[0057] XD π = AX + BΥ…(3)

[0058] The matrix D on the left side of equation (3) π is a matrix with multiple weights as components, and X corresponds to the observed temperature data. If the values of the components of matrix D π are determined, the operation on the left side of equation (3) can be performed. If the value on the left side of equation (3) is determined, the coefficients A and B on the right side of equation (3) can be calculated by the method of dynamic mode decomposition including control input.

[0059] Therefore, in the information processing system of this embodiment, the conversion based on the non-integer order differential equation is adopted as the conversion π. If based on the Caputo differential, which is one of the definitions of the non-integer order differential equation, the conversion D(α) corresponding to the non-integer order differential equation in the case of the differential order being α is represented by the following equation (4). Among them, equation (4) is the definition when α is not a positive integer. In addition, in equation (4), m is the number of time points, is the m×m matrix expression of the l-th order integer differential.

[0060] [Number 4]

[0061]

[0062] In addition, the weight w included in equation (4) is represented by the following equation (5). In addition, Γ(ν) in equation (5) is the gamma function.

[0063] [Number 5]

[0064]

[0065] In the conversion D of the non-integer order differential equation represented by equation (4) (α) , if the differential order α is determined, the values of the components of its matrix are determined, so the operation on the left side of equation (3) can be performed. The information processing system of this embodiment performs the following processing: taking the differential order α of the non-integer order differential equation as the first parameter, taking the coefficients A and B on the right side of equation (3) as the second parameters, and using dynamic mode decomposition to calculate the parameters of these models.

[0066] In addition, the above formula is a diagram illustrating an example of an implementation method for a non-integer order differential equation, and the implementation method is not limited to the method represented by the above formula. For example, an implementation method using a high-order difference method can also be adopted. Additionally, for example, an implementation method using a non-integer order integral can also be adopted, and the same effect can be expected when these implementation methods are adopted. Moreover, various implementation methods other than these can also be adopted.

[0067] <Parameter Calculation Process>

[0068] In the information processing system of this embodiment, a plurality of candidate values are prepared in advance for the differential order α as the first parameter. The candidate values of the first parameter are, for example, preset in advance by a user, administrator, or designer of the information processing system of this embodiment, and stored in the storage unit 12 of the information processing device 1 as a setting file or the like. The setting of the candidate values can be performed, for example, by listing the candidate values such as "α = 1.00, 1.01, 1.02,..., 1.99", and additionally, for example, it can be performed by setting conditions such as "minimum value 1.00, maximum value 1.99, interval 0.01", and can be performed by various methods other than these.

[0069] The information processing device 1 obtains one candidate value from the plurality of candidate values of the differential order α as the first parameter. The information processing device 1 calculates the value on the left side of the above formula (3), that is, the time evolution data, based on the obtained candidate value of the differential order α, the above formulas (4) and (5), and the time series of observed temperature data stored in the process DB 12b. The value calculated at this time is used as the true value of the time evolution data.

[0070] After calculating the value on the left side of formula (3), the information processing device 1 performs a dynamic mode decomposition with control input using the time series of control input data and observed temperature data stored in the process DB 12b. Thereby, the information processing device 1 can calculate the second parameters included on the right side of formula (3), that is, the values of matrices A and B.

[0071] Next, the information processing device 1 calculates the predicted value of the time evolution data by performing the operation on the right side of formula (3) with the calculated A and B set for the time series of control input data and observed temperature data stored in the process DB 12b. The information processing device 1 calculates the error (such as the mean square error or the mean absolute error, etc.) between the true value and the predicted value of the calculated time evolution data. Thereby, the information processing device 1 can obtain one candidate value of the first parameter α, the second parameters A and B, and the predicted error.

[0072] The information processing device 1 performs the same processing on multiple candidate values of the set first parameter α, calculates the second parameters A and B and the error for all candidate values of the first parameter α. The information processing device 1 compares all the calculated errors, obtains the first parameter α and the second parameters A and B corresponding to the minimum error, and outputs the obtained parameters as the calculation result of the parameters of the model.

[0073] Figure 3 It is a flowchart showing the process of the parameter calculation process performed by the information processing device 1 of the present embodiment. The parameter calculation unit 11c of the processing unit 11 of the information processing device 1 of the present embodiment reads multiple candidate values of the first parameter α stored in the storage unit 12 generated in advance (step S1).

[0074] The parameter calculation unit 11c obtains one candidate value from the multiple candidate values of the first parameter α read in step S1 (step S2). The parameter calculation unit 11c calculates the time evolution data of the observed temperature data based on the non-integer order differential equation in which the first parameter α obtained in step S2 is set and the time series of observed temperature data stored in the process DB 12b (step S3).

[0075] The parameter calculation unit 11c calculates the second parameters A and B by performing dynamic mode decomposition including control input based on the time evolution data calculated in step S3, the time series of control input data stored in the process DB 12b, and the observed temperature data (step S4).

[0076] The parameter calculation unit 11c performs the operation on the right side of equation (3) based on the second parameters A and B calculated in step S4, the time series of control input data stored in the process DB 12b, and the observed temperature data to calculate the predicted value of the time evolution data. The parameter calculation unit 11c calculates the error E between the predicted value of the calculated time evolution data and the true value of the time evolution data calculated in step S3 (step S5). The parameter calculation unit 11c associates the candidate value of the first parameter α obtained in step S2, the second parameters A and B calculated in step S4, and the error E calculated in step S5 and stores them in the storage unit 12 (step S6).

[0077] The parameter calculation unit 11c determines whether the processing of steps S2 to S6 has been completed for all the candidate values read in step S1 (step S7). If the processing has not been completed for all the candidate values (S7: No), the parameter calculation unit 11c returns the processing to step S2, obtains other candidate values, and performs the processing of S2 to S6.

[0078] When the processing for all the candidate values is completed (S7: Yes), the parameter calculation unit 11c searches for the minimum error from among the multiple errors E calculated in step S5 for each candidate value (step S8). The parameter calculation unit 11c adopts the first parameter α and the second parameters A and B corresponding to the minimum error E searched in step S8 as the parameters of the model (step S9), and ends the processing.

[0079] The parameters calculated by the information processing apparatus 1 are determined by the time evolution model represented by equation (3). By using this time evolution model, it is possible to expect to perform various processes such as prediction of the operation of the substrate processing apparatus 3, control of the operation of the substrate processing apparatus 3, or abnormality determination of the substrate processing apparatus 3.

[0080] <Abnormality determination process>

[0081] Figure 4 is a flowchart showing the process of the abnormality determination process performed by the information processing apparatus 1 in the present embodiment. The control processing unit 11a of the processing unit 11 of the information processing apparatus 1 in the present embodiment starts substrate processing such as etching of a wafer by, for example, accepting an operation for starting processing by the user (step S21).

[0082] 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 S22). The data acquisition unit 11b stores the control input data and the observed temperature data acquired in step S22 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 S23).

[0083] The data acquisition unit 11b determines whether the substrate processing for the wafer has ended (step S24). If the substrate processing has not ended (S24: No), the data acquisition unit 11b returns the processing to step S22 and repeats the acquisition and storage of data.

[0084] If the substrate processing has ended (S24: 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 S25).

[0085] The parameter calculation unit 11c of the processing unit 11 calculates the parameters of the model using dynamic mode decomposition based on the information of the candidate values of the differential order α prepared in advance and the time-series control input data and observed temperature data acquired in step S25 (step S26). In addition, the processing performed in this step S26 corresponds to Figure 3The parameter calculation process shown in the flowchart.

[0086] The abnormality determination unit 11d of the processing unit 11 compares the parameters of the model calculated in step S26 with a predetermined threshold value (step S27). Based on the comparison between the parameters of the model and the threshold value, the abnormality determination unit 11d determines whether there is an abnormality in the substrate processing implemented this time (step S28). When there is an abnormality (S28: Yes), the display processing unit 11e of the processing unit 11 notifies the user of the abnormality by displaying a message indicating that an abnormality has been detected on the display unit 14 (step S29), and ends the processing. When there is no abnormality (S28: No), the processing unit 11 ends the processing.

[0087] <Modification Example>

[0088] In the above-described embodiment, the temperature control of the substrate processing apparatus 3 has been described as an example, but the application of the present technology is not limited to temperature control. Figure 5 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, for example, a system for determining abnormalities in the substrate processing apparatus 3 that transports wafers.

[0089] 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, for example, an actuator or a motor 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 correspondingly, the movable part 3b moves to transfer the wafer.

[0090] In addition, the substrate processing apparatus 3 includes a sensor for measuring the position and the like. The information processing apparatus 1 acquires the measurement result of the position of the movable part 3b by the sensor of the substrate processing apparatus 3 as the observation position data at a predetermined cycle. In addition, in this modification example, it is assumed that the 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. In addition, when the movable part 3b rotates, for example, the rotational speed or angular velocity may be measured by the sensor. In addition, the information processing apparatus 1 may acquire the image data of the movable part 3b photographed by a camera instead of the sensor. In addition, the information processing apparatus 1 may also acquire the information obtained by combining these multiple pieces of information.

[0091] The information processing apparatus 1 acquires the control input data and the observation position data at a predetermined cycle and stores them in the process DB 12b. After the substrate processing apparatus 3 finishes transferring the wafer, the information processing apparatus 1 can calculate the parameters of the model based on the time-series control input data and observation position data stored in the process DB 12b by the above process, and perform processing such as abnormality determination based on the calculated parameters.

[0092] 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.

[0093] <Modified Example 2>

[0094] The above information processing system uses the non-integer order differential equation shown in (4) as the transformation π, but the transformation π is not limited to non-integer order differentiation. Any transformation can be used as long as the transfer function satisfies the causality law. The transfer function can be various functions such as a function representing the lag effect of the system to be targeted, an exponential function, a logarithmic function, a polynomial, a trigonometric function, a piecewise-defined function, a function generated by their sum or product, or a function generated by machine learning, etc., which are determined experimentally or theoretically. In addition, the transfer function can also be a function that probabilistically determines the transformed value, etc., provided as a probability distribution.

[0095] In Modified Example 2, the transformation function represented by the matrix D shown in the following (6) is used as an example of various transformation functions, and the method of optimizing the values of a and b included in the matrix D using the time series observed temperature data for the information processing system is described. In addition, D of the transformation function in (6) is an example and is not limited thereto. For example, D can be independent for all components, or can be a restricted matrix such as a matrix in which the same values are arranged from the upper left to the lower right. π as an example of various transformation functions, and the method of optimizing the values of a and b included in the matrix D using the time series observed temperature data for the information processing system is described. In addition, D of the transformation function in (6) is an example and is not limited thereto. For example, D can be independent for all components, or can be a restricted matrix such as a matrix in which the same values are arranged from the upper left to the lower right. π is an example and is not limited thereto. For example, D π is an example and is not limited thereto. For example, D π can be independent for all components, or can be a restricted matrix such as a matrix in which the same values are arranged from the upper left to the lower right.

[0096] [Equation 6]

[0097]

[0098] The information processing apparatus 1 in Modified Example 2 sets an appropriate initial value for the matrix D of the transfer function, and calculates the coefficients A and B in (3) by the dynamic mode decomposition method based on the above (1) to (3). Then, the information processing apparatus 1 calculates the left and right sides of (3) using the time series observed temperature data and the control input data, calculates the error therebetween, and updates the matrix D, for example, using the existing steepest descent method or the like based on the error. π The information processing apparatus 1 calculates the left and right sides of (3) using the time series observed temperature data and the control input data, calculates the error therebetween, and updates the matrix D, for example, using the existing steepest descent method or the like based on the error. π . The information processing apparatus 1 updates the matrix D by repeatedly performing the above process π so that the calculated error falls within a desired range, and thus can finally optimize the components a and b of D. π

[0099] Figure 6This is a flowchart showing the process of parameter calculation processing performed by the information processing apparatus 1 of Modification 2. The parameter calculation unit 11c of the processing unit 11 of the information processing apparatus 1 of Modification 2 sets appropriate initial values for the components a and b of the matrix D of the transfer function (step S41). In addition, the initial values of a and b can be, for example, values predetermined by a user or the like, and can also be, for example, values based on random numbers, or values determined by methods other than these. π The parameter calculation unit 11c calculates the time evolution data of the observed temperature data based on the matrix D set in step S1

[0100] and the time series of observed temperature data stored in the process DB 12b (step S42). The parameter calculation unit 11c uses the time evolution data calculated in step S42, the time series of control input data stored in the process DB 12b, and the observed temperature data to perform dynamic mode decomposition with control input based on the above formula (3) to calculate the parameters A and B (step S43). π The parameter calculation unit 11c calculates the predicted value of the time evolution data by performing the operation on the right side of formula (3) based on the parameters A and B calculated in step S43, the time series of control input data stored in the process DB 12b, and the observed temperature data. The parameter calculation unit 11c calculates the error between the predicted value of the time evolution data thus calculated and the time evolution data calculated in step S42 (step S44).

[0101] The parameter calculation unit 11c determines whether the error calculated in step S44 is less than a predetermined threshold value (step S45). When the error is equal to or greater than the threshold value (S45: No), the parameter calculation unit 11c updates the values of the components a and b of the matrix D

[0102] to make the error smaller, for example, by the steepest descent method based on the differential of the error calculated in step S44 (step S46), returns the process to step S42, and repeats the above process. π When the error is less than the threshold value (S45: Yes), the parameter calculation unit 11c sets the components a and b of the matrix D and the parameters A and B at that time to the optimal values, stores these values in the storage unit 12 (step S47), and ends the process.

[0103] In addition, when updating the matrix D π the sum or average of the errors calculated for multiple time series data can also be used. For example, in the case of multiple time series data that are expected to be represented by the same matrix D

[0104] but the coefficient matrices A and B can be different, by π the sum or average of the errors calculated for multiple time series data can also be used. For example, in the case of multiple time series data that are expected to be represented by the same matrix D π but the coefficient matrices A and B can be different, by Figure 6The error calculated in step S44 of the flowchart shown can also be calculated using functions such as the sum or average of the errors in the case of using the optimal coefficient matrices A and B for these time series data. This also applies when the coefficient matrices A and B have the same values among multiple time series data.

[0105] In addition, the information processing apparatus 1 of the above-described modification example 2 Figure 6 In step S44 of the flowchart shown, calculates the time evolution data on the left side of equation (3) using matrix D π and the predicted value of the time evolution data on the right side of equation (3) using the calculated parameters A and B, and calculates the error between the two time evolution data. However, the information processing apparatus 1 can directly calculate based on the parameters A and B without using the calculated parameters A and B to calculate the predicted value of the time evolution data.

[0106] If the value obtained by arranging all components of the matrices of parameters A and B in sequence and vectorizing is set as θ (refer to the following equation (7)), the calculated error L(θ) becomes equation (8). In addition, in equation (8), the right side is the Frobenius norm of the matrix. Also, π(x) is the time evolution data calculated based on matrix D π and the observed data X.

[0107] [Equation 7]

[0108] θ = [A 11 , A 12 ,..., B 11 , B 12 ,...]…(7)

[0109]

[0110] The information processing apparatus 1 calculates the constant term c, the first-order differential J, and the second-order differential H of the error shown in the following equations (9) to (11) for the error L(θ) defined by equation (8).

[0111] [Equation 8]

[0112] c = L(0)…(9)

[0113]

[0114] The information processing apparatus 1 can calculate the minimum error L π when only optimizing the parameters A and B by performing the operation of the following equation (12) based on the calculated constant term c, first-order differential J, and second-order differential H. * . In addition, in equation (12), the superscript "T" represents the transposed matrix, and the superscript "+" represents the generalized inverse matrix.

[0115] [Number 9]

[0116]

[0117] The information processing device 1 can Figure 6 calculate the error L based on equation (12) in step S44 of the flowchart shown * and update the matrix D through step S46 using the calculated L * π .

[0118] <Summary>

[0119] In the information processing system of the present embodiment configured as above, the information processing device 1 acquires time-series observed temperature data related to the substrate processing device 3 as the target device, and calculates the first parameter and the second parameter of the model for predicting the time evolution data of the observed data based on the observed data through dynamic mode decomposition of the acquired observed temperature data. The first parameter of the model can be the parameter D related to the function for converting the observed temperature data into time evolution data π . The second parameter of the model can be the parameter A related to the function for interpreting the observed data of the time evolution data. Thus, it is expected that the information processing system can generalize dynamic mode decomposition to generate a model with better accuracy, and it is expected to effectively utilize the data obtained from the substrate processing device 3.

[0120] In addition, in the information processing system of the present embodiment, the function for converting the observed temperature data into time evolution data is a function represented by a non-integer order differential equation, and the first parameter includes the differential order α of the non-integer order differential equation. Thus, the information processing system can determine the conversion function by setting the differential order α, so it is expected to reduce the number of parameters to be calculated.

[0121] Furthermore, in the present embodiment, a non-integer order differential equation is adopted as the conversion function, but it is not limited thereto. The conversion function can be various functions such as an exponential function, a logarithmic function, a polynomial, a trigonometric function, a function defined by sections, a Gaussian distribution having a specific positive value distributed with a specific time difference as an average, a function generated by their sum or product, or a function generated by machine learning, etc.

[0122] The embodiments disclosed this time are illustrative in all aspects 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 the meaning equivalent to the claims and all changes within the scope.

[0123] The matters described in each embodiment can be combined with each other. In addition, the independent claims and dependent claims recited in the claims can be combined with each other in all combinations regardless of the citation form. Further, although the claims use a form of a claim that recites and cites two or more other claims (multiple dependent claim form), it is not limited thereto, and a form of a multiple dependent claim (multiple cited item dependent claim) that recites and cites at least one multiple dependent claim may also be used.

[0124] Description of Reference Numerals

[0125] 1 Information processing device (computer); 3 Substrate processing device; 3a Electrostatic chuck; 3b Movable part; 11 Processing unit; 11a Control processing unit; 11b Data acquisition unit (acquisition unit); 11c Parameter calculation 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: Obtain time-series observation data related to an object device; and Calculate a first parameter and a second parameter of a model by dynamic mode decomposition based on the obtained observation data, where the above model is a model for predicting the time-evolution data of the above observation data based on the observation data, the above first parameter is a parameter related to a conversion function for converting the above observation data into the above time-evolution data, the above second parameter is a parameter related to a function for explaining the above observation data of the above time-evolution data.

2. The information processing method according to claim 1, wherein, the above conversion function is a function represented by a non-integer order differential equation, the above first parameter includes the order of the above non-integer order differential equation.

3. The information processing method according to claim 1, wherein, Obtain time-series control input data for the above object device and the above observation data corresponding to the above control input data, Calculate the first parameter and the second parameter of the above model by dynamic mode decomposition based on the obtained control input data and observation data, the above second parameter is a parameter related to a function for explaining the above control input data and the above observation data of the above time-evolution data.

4. The information processing method according to claim 3, wherein, the above second parameter includes a coefficient matrix for the above control input data and a coefficient matrix for the above observation data.

5. The information processing method according to claim 1, wherein, Obtain a plurality of candidate parameters related to the above first parameter, Calculate the above second parameter corresponding to each candidate parameter of the above first parameter respectively by dynamic mode decomposition based on the obtained control input data and observation data, Perform prediction based on the above model for each group of the candidate parameters of the above first parameter and the corresponding above second parameter, calculate the predicted value of each candidate parameter, Calculate the above time-evolution data based on the obtained above observation data, Determine the above first parameter from the above plurality of candidate parameters based on the error between the predicted value of the above time-evolution data for each candidate parameter and the above time-evolution data calculated based on the above observation data.

6. The information processing method according to claim 1, wherein, Set an initial value for the above first parameter, Calculate the above second parameter corresponding to the above first parameter with the above initial value set respectively by dynamic mode decomposition based on the obtained control input data and observation data, Calculate an error related to the time-evolution data output by the above model based on the calculated above second parameter, Update the calculated above error to update the above first parameter.

7. The information processing method according to claim 1, wherein, Determine the state of the above object device based on the calculated parameters.

8. The information processing method according to claim 3, wherein, the above object device is a substrate processing device, Obtain time-series control input data for the above substrate processing device and time-series observation data based on sensors provided on the above substrate processing device.

9. A computer program that causes a computer to perform the following processing: Obtain time-series observation data related to an object device; and Calculate a first parameter and a second parameter of a model by performing dynamic mode decomposition based on the obtained observation data, where the model is a model for predicting time-evolution data of the observation data based on the observation data, The first parameter is a parameter related to a conversion function that converts the observation data into the time-evolution data, The second parameter is a parameter related to a function of the observation data that interprets the time-evolution data.

10. An information processing apparatus, comprising: An acquisition unit that acquires time-series observation data related to an object device; and A calculation unit that calculates a first parameter and a second parameter of a model by performing dynamic mode decomposition based on the obtained observation data, where the model is a model for predicting time-evolution data of the observation data based on the observation data, The first parameter is a parameter related to a conversion function that converts the observation data into the time-evolution data, The second parameter is a parameter related to a function of the observation data that interprets the time-evolution data.

Images