Information processing apparatus, substrate processing apparatus, and film thickness prediction method

Abstract

This technology provides a method for more accurately predicting film thickness data at multiple prediction points on the substrate surface. [Solution] The above problem is solved by an information processing device having an acquisition unit that acquires measured film thickness data at multiple measurement points on the surface of a substrate formed by a substrate processing device, a prediction model creation unit that creates a prediction model by regressing the measured film thickness data with Zernike polynomials, a prediction unit that predicts film thickness data at multiple prediction points on the substrate surface using the prediction model and outputs it as predicted film thickness data, and a display control unit that displays the predicted film thickness data on an output device.

Description

[Technical Field]

[0001] This disclosure relates to an information processing device, a substrate processing device, and a film thickness prediction method. [Background technology]

[0002] In a substrate processing apparatus, a film deposition process is performed on a substrate. The film thickness deposited on the substrate is measured by a measuring device such as a film thickness gauge after the film deposition process is completed (see, for example, Patent Document 1).

[0003] The film thickness measured by the measuring device is used as an indicator for quality control. Generally, since measuring film thickness is time-consuming, the number of measurement points on the substrate surface used for film thickness measurement in the mass production process is less than the number of measurement points used for film thickness measurement in the evaluation process. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2024-140711 [Overview of the initiative] [Problems that the invention aims to solve]

[0005] This disclosure provides a technology for predicting film thickness data at multiple prediction points on a substrate surface with higher accuracy. [Means for solving the problem]

[0006] One aspect of the present disclosure is an information processing apparatus comprising: an acquisition unit that acquires measured film thickness data at multiple measurement points on the surface of a substrate formed by a substrate processing apparatus; a prediction model creation unit that creates a prediction model by regressing the measured film thickness data with a Zernike polynomial; a prediction unit that predicts film thickness data at multiple prediction points on the substrate surface using the prediction model and outputs it as predicted film thickness data; and a display control unit that displays the predicted film thickness data on an output device. [Effects of the Invention]

[0007] According to the present disclosure, the film thickness data of a plurality of prediction points on the substrate surface can be predicted with higher accuracy.

Brief Description of the Drawings

[0008] [Figure 1] It is a configuration diagram of an example of a film thickness prediction system according to the present embodiment. [Figure 2] It is a hardware configuration diagram of an example of a computer. [Figure 3] It is a diagram for explaining an example of problems in the mass production process of a substrate. [Figure 4] It is a diagram for explaining an example of problems in the mass production process of a substrate. [Figure 5] It is an explanatory diagram of an example of a film thickness prediction function for predicting film thickness data at an arbitrary coordinate from a small number of measured film thickness data with higher accuracy. [Figure 6] It is an explanatory diagram of an example of a film thickness prediction function for predicting film thickness data around a chip from measured film thickness data during mass production with higher accuracy. [Figure 7] It is a functional block diagram of an example of an apparatus controller according to the present embodiment. [Figure 8] It is a flowchart of an example of the processing of a film thickness prediction system according to the present embodiment. [Figure 9] It is an explanatory diagram of an example of an algorithm of a film thickness prediction function. [Figure 10] It is an explanatory diagram of an example of an algorithm of a film thickness prediction function. [Figure 11] It is an explanatory diagram of an example of an algorithm of a film thickness prediction function. [Figure 12] It is an explanatory diagram of an example of an algorithm of a film thickness prediction function. [Figure 13] It is an explanatory diagram of an example of an algorithm of a film thickness prediction function. [Figure 14] It is a graph showing an example of the result of a pre - actual comparison between the statistical value of the in - plane film thickness of the substrate based on 49 true values and the statistical value of the in - plane film thickness of the substrate based on 49 predicted values.

Modes for Carrying Out the Invention

[0009] Hereinafter, this embodiment will be described with reference to the drawings.

[0010] <System Configuration> FIG. 1 is a configuration diagram of an example of a film thickness prediction system according to this embodiment. The film thickness prediction system 1 shown in FIG. 1 includes a substrate processing apparatus 10, a measuring apparatus 11, an apparatus controller 12, a server apparatus 14, a database apparatus 15, and an operator terminal 16. The substrate processing apparatus 10, the measuring apparatus 11, and the apparatus controller 12 are installed in the manufacturing factory 2. Also, the server apparatus 14, the database apparatus 15, and the operator terminal 16 may be installed in the manufacturing factory 2 or may be installed outside the manufacturing factory 2. The substrate processing apparatus 10, the measuring apparatus 11, the apparatus controller 12, the server apparatus 14, the database apparatus 15, and the operator terminal 16 are communicably connected via networks N1 and N2 such as the Internet and a LAN (Local Area Network).

[0011] The substrate processing apparatus 10 is an apparatus that forms a film on the surface of a substrate such as a wafer. The substrate processing apparatus 10 executes a process of forming a film on the surface of the substrate. The substrate processing apparatus 10 executes a process of forming a film on the surface of the substrate according to a process recipe in which the procedure of the process is shown. Note that the substrate processing apparatus 10 may be a film forming apparatus, a semiconductor manufacturing apparatus, or a heat treatment apparatus.

[0012] The substrate processing apparatus 10 receives control commands from the apparatus controller 12 according to the process recipe and executes a process of depositing a film on the substrate surface. As shown in Figure 1, the substrate processing apparatus 10 may have the apparatus controller 12 installed, or it may not necessarily have the apparatus controller 12 installed as long as it is connected in a communicative manner. The apparatus controller 12 causes the substrate processing apparatus 10 to execute the process according to the process recipe by outputting control commands that control the adjustment items (control components) of the substrate processing apparatus 10 according to the process recipe. The apparatus controller 12 has a human-machine interface function that receives instructions for the substrate processing apparatus 10 from the operator and provides information about the substrate processing apparatus 10 to the operator. The apparatus controller 12 acquires various information necessary for processing the film thickness prediction system 1 according to this embodiment from the substrate processing apparatus 10, the measuring device 11, the server device 14, the database device 15, or the operator terminal 16, and processes it.

[0013] The measuring device 11 measures film thickness data at multiple measurement points on the substrate surface deposited by the substrate processing device 10. Hereinafter, the film thickness data at the measurement points on the substrate surface measured by the measuring device 11 will be referred to as the measured film thickness data. The measured film thickness data represents the degree of film deposition on the substrate surface as measured by the measuring device 11.

[0014] The measuring device 11 may transmit the measured film thickness data to the substrate processing device 10, the device controller 12, the server device 14, the database device 15, or the worker terminal 16 via networks N1 and N2. Alternatively, the worker may provide the measured film thickness data to the substrate processing device 10, the device controller 12, the server device 14, the database device 15, or the worker terminal 16 using a portable storage device such as a USB (Universal Serial Bus) memory.

[0015] Generally, measuring film thickness data using the measuring device 11 is time-consuming. For this reason, in mass production processes for substrates such as semiconductor manufacturing, film thickness data is measured at fewer measurement points than in the evaluation process (for example, 49 points), such as 13 measurement points on the substrate surface.

[0016] The database device 15 stores and manages various information necessary for processing the film thickness prediction system 1 according to this embodiment. The database device 15 may also store and manage the measured film thickness data of measurement points in past evaluation processes as verification data.

[0017] The server device 14 acquires various information necessary for processing the film thickness prediction system 1 according to this embodiment from the substrate processing device 10, the measuring device 11, the device controller 12, the database device 15, or the operator terminal 16, and processes it.

[0018] The operator terminal 16 is a PC (Personal Computer) or smartphone, etc., operated by an operator such as the operator or analyst of the substrate processing apparatus 10. For example, the operator terminal 16 acquires various information necessary for processing the film thickness prediction system 1 according to this embodiment from the substrate processing apparatus 10, the measuring device 11, the device controller 12, the server device 14, or the database device 15, and processes it. The operator terminal 16 may transmit the operator's operations to the device controller 12 or the server device 14, and receive and display the processing results from the device controller 12 or the server device 14.

[0019] It should be noted that the film thickness prediction system 1 shown in Figure 1 is just one example, and there are various system configurations depending on the application and purpose. At least part of the processing of the server device 14 may be performed by the device controller 12 or the operator terminal 16. The device controller 12, the server device 14, or the operator terminal 16 are examples of information processing devices that perform the film thickness prediction method of this embodiment. The substrate processing device 10 on which the device controller 12 is mounted is an example of a substrate processing device 10 that performs the film thickness prediction method of this embodiment. The server device 14 may be implemented by multiple information processing devices, or it may be implemented as a cloud computing service.

[0020] Furthermore, the film thickness prediction system 1 shown in Figure 1 may be implemented using a standalone substrate processing apparatus 10 and apparatus controller 12. The film thickness prediction system 1 may have a configuration in which at least a part of the server apparatus 14, database apparatus 15, and operator terminal 16 are integrated, or it may have a further separated configuration, or a configuration in which some parts are omitted.

[0021] <Hardware Configuration> The device controller 12, server device 14, database device 15, and worker terminal 16 are implemented by a computer 500 with the hardware configuration shown in Figure 2. Figure 2 is a hardware configuration diagram of an example of computer 500.

[0022] The computer 500 in Figure 2 includes an input device 501, an output device 502, an external interface 503, RAM (Random Access Memory) 504, ROM (Read Only Memory) 505, a CPU (Central Processing Unit) 506, a communication interface 507, and an HDD (Hard Disk Drive) 508, all of which are interconnected via bus B. The input device 501 and output device 502 may be connected and used only when necessary.

[0023] The input device 501 is a keyboard, mouse, touch panel, etc., and is used by operators to input various operation signals. The output device 502 is a display, etc., which displays the processing results from the computer 500. The communication I / F 507 is an interface that connects the computer 500 to network N1 or N2. The HDD 508 is an example of a non-volatile storage device that stores programs and data. The CPU 506 is an example of a processor and may have a device such as a GPU (Graphics Processing Unit).

[0024] External I / F 503 is an interface to external devices. Computer 500 can read from and / or write to recording media 503a such as an SD (Secure Digital) memory card via External I / F 503. ROM 505 is an example of a non-volatile semiconductor memory (storage device) that stores programs and data. RAM 504 is an example of a volatile semiconductor memory (storage device) that temporarily holds programs and data.

[0025] The CPU 506 is a processing unit that reads programs and data from storage devices such as the ROM 505 and HDD 508 onto the RAM 504 and executes processing, thereby realizing the overall control and functions of the computer 500. Note that the CPU 506 is just one example of a processor and may also have devices such as a GPU (Graphics Processing Unit).

[0026] The device controller 12, server device 14, database device 15, and worker terminal 16 shown in Figure 1 can implement various functions described later by running a program on a computer 500 with the hardware configuration shown in Figure 2, for example.

[0027] <Challenges in the mass production process> Figure 3 illustrates an example of a challenge in the mass production process of substrates. For example, in the substrate evaluation process, there are 49 measurement points on the substrate surface. On the other hand, in the mass production process of substrates, there are 13 measurement points on the substrate surface. Generally, the number of measurement points in the mass production process of substrates is fewer than the number of measurement points in the evaluation process of substrates, taking into account the time required to measure film thickness data.

[0028] Because the number of measurement points in the mass production process of a substrate is fewer than the number of measurement points in the evaluation process of a substrate, the statistical values ​​of the substrate surface film thickness (in-plane film thickness) based on the film thickness data from the measurement points in the mass production process (average film thickness, range, or in-plane uniformity) may differ from the statistical values ​​of the in-plane film thickness based on the film thickness data from the measurement points in the evaluation process.

[0029] Therefore, statistical values ​​of in-plane film thickness based on film thickness data from measurement points in the mass production process may be unsuitable as an indicator for quality control. Furthermore, interpolating in-plane film thickness using film thickness data from measurement points in the mass production process may result in lower accuracy compared to interpolating using film thickness data from measurement points in the evaluation process. Figure 3 shows that the predicted in-plane film thickness obtained by interpolating film thickness data from 49 measurement points in the evaluation process differs from the predicted in-plane film thickness obtained by interpolating film thickness data from 13 measurement points in the mass production process. Thus, as the number of measurement points on the substrate surface decreases, the accuracy of the interpolation results for film thickness data from points other than the measurement points deteriorates.

[0030] Figure 4 illustrates an example of a challenge in the mass production process of a substrate. Figure 4 shows the relationship between the locations where chips are formed on the substrate and 13 measurement points in the mass production process. As shown in Figure 4, the 13 measurement points in the mass production process cannot measure the entire film thickness in the chip formation locations. The chip formation locations are an example of a critical area for quality control. However, measuring the entire film thickness in critical areas such as chip formation locations is difficult from a productivity standpoint.

[0031] Furthermore, while film thickness can be estimated by interpolation such as linear interpolation, the accuracy of interpolation tends to deteriorate at predicted points far from the measurement points. In addition, with 13 measurement points in a mass production process, it may be necessary to rely on extrapolation depending on the distribution of the measurement points, raising concerns that the accuracy of interpolation may deteriorate even further.

[0032] Therefore, in this embodiment, the film thickness data for an arbitrary coordinate is predicted with higher accuracy from the film thickness data of the number of measurement points in the mass production process of the substrate, which is fewer than the number of measurement points in the substrate evaluation process.

[0033] Figure 5 is an explanatory diagram of an example of a film thickness prediction function that predicts film thickness data at arbitrary coordinates with higher accuracy from a small number of measured film thickness data points. The film thickness prediction function in Figure 5 takes measured film thickness data from a number of measurement points smaller than the number of prediction points as input, and creates a prediction model by regressing the input measured film thickness data with a Zernike polynomial. The film thickness prediction function uses the created prediction model to predict the film thickness data at arbitrary coordinates on the substrate. The details of the processing of the film thickness prediction function will be described later.

[0034] In this embodiment, as shown in Figure 5, the film thickness data for a desired coordinate can be predicted with higher accuracy even from measurement film thickness data from fewer measurement points than the number of prediction points.

[0035] Figure 6 is an explanatory diagram of an example of a film thickness prediction function that predicts film thickness data around the chip with higher accuracy from measured film thickness data during mass production. The film thickness prediction function in Figure 6 takes measured film thickness data from mass production, which has fewer measurement points than during evaluation, as input, and creates a prediction model by regression on the input measured film thickness data with Zernike polynomial. The film thickness prediction function uses the created prediction model to predict the film thickness data around the chip on the substrate. The details of the processing of the film thickness prediction function will be described later.

[0036] In this embodiment, as shown in Figure 6, the film thickness data near each chip can be predicted with higher accuracy even from a smaller number of mass production measurement film thickness data than the number of prediction points. Therefore, in this embodiment, correlation analysis between film thickness and yield for each chip becomes possible, enabling more accurate quality control.

[0037] <Functional Configuration> The following describes an example of an information processing device, specifically a device controller 12, that uses a prediction model to predict film thickness data at multiple prediction points on the substrate surface and outputs it as predicted film thickness data. The information processing device that uses a prediction model to predict film thickness data at multiple prediction points on the substrate surface and outputs it as predicted film thickness data may also be a server device 14 or an operator terminal 16.

[0038] The device controller 12 of the film thickness prediction system 1 according to this embodiment is implemented using a functional block as shown in Figure 7, for example. Figure 7 is a functional block diagram of an example of the device controller 12 according to this embodiment. Note that the functional block diagram in Figure 7 omits the illustration of components that are not necessary for the explanation of this embodiment.

[0039] The device controller 12 shown in Figure 7 implements an acquisition unit 50, a storage unit 52, a prediction model creation unit 54, a prediction unit 56, an input reception unit 58, and a display control unit 60 by executing a program for the device controller 12.

[0040] The acquisition unit 50 acquires measurement film thickness data from multiple measurement points on the substrate surface deposited by the substrate processing apparatus 10. The acquisition unit 50 acquires measurement film thickness data from multiple measurement points on the substrate surface from the measurement device 11 or the database device 15, etc. The acquisition unit 50 records the measurement film thickness data from multiple measurement points on the substrate surface in the storage unit 52.

[0041] The prediction model creation unit 54 creates a prediction model by regression on the measured film thickness data using the Zernike polynomial, as described below. The prediction unit 56 uses the prediction model created by the prediction model creation unit 54, as described below, to predict the film thickness data at multiple prediction points on the substrate surface and outputs it as predicted film thickness data.

[0042] The input receiving unit 58 receives various operations from the operator. For example, operations received from the operator include launching an application and performing various operations on the launched application. The input receiving unit 58 notifies the prediction model creation unit 54, the prediction unit 56, and the display control unit 60 of the content of the various operations from the operator. The input receiving unit 58 may also receive input from the operator for multiple prediction points on the substrate surface.

[0043] The display control unit 60 displays the predicted film thickness data output by the prediction unit 56 on the output device according to the content of various operations performed by the operator. The display control unit 60 may display the predicted film thickness data for multiple prediction points on the substrate surface output by the prediction unit 56 in a tabular format, or it may display it as an image diagram in which the film thickness on the substrate surface can be identified by color or the like.

[0044] <Processing> Figure 8 is a flowchart showing an example of the processing of the film thickness prediction system 1 according to this embodiment.

[0045] In step S10, the acquisition unit 50 of the device controller 12 acquires measured film thickness data at multiple measurement points on the substrate surface deposited by the substrate processing apparatus 10. For example, the acquisition unit 50 acquires measured film thickness data at multiple measurement points on the substrate surface from the measuring device 11. The acquisition unit 50 may also acquire measured film thickness data at multiple measurement points on the substrate surface from a database device 15 that stores and manages measured film thickness data at multiple measurement points on the substrate surface measured by the measuring device 11. The acquisition unit 50 may also acquire the measured film thickness data at multiple measurement points on the substrate surface measured by the measuring device 11 via a portable storage device such as a USB memory.

[0046] In step S12, the prediction model creation unit 54 of the device controller 12 creates a prediction model by regressing the measured film thickness data using the Zernike polynomial. Here, the details of the process in step S12 will be explained with reference to Figures 9 to 13.

[0047] Figures 9 to 13 are explanatory diagrams illustrating an example of the algorithm for the film thickness prediction function.

[0048] The prediction model creation unit 54 creates a prediction model by regressing the measured film thickness data using the Zernike polynomial in equation (1) below. y represents the film thickness. X represents the design matrix. z i This represents the Zernike coefficient. Also, λ i This indicates the normalization coefficient.

[0049]

number

[0050] The design matrix X is constructed as follows. Note that r i Let θ be the radius vector of the i-th measurement point (normalized to 0 ≤ r ≤ 1). i Let be the deflection angle of the i-th measurement point.

[0051]

number

[0052] The prediction model creation unit 54 performs regression (fitting) on ​​a small number of measured film thickness data obtained in step S10 using a Zernike polynomial. As shown in Figure 9, the combination of the Zernike coefficients obtained by regression on the small number of measured film thickness data obtained in step S10 using a Zernike polynomial and the Zernike polynomial used for regression is used as a prediction model, and the in-plane distribution of film thickness on the substrate surface is predicted using this prediction model.

[0053] The Zernike coefficients used in the regression in step S10 have characteristics such as those shown in Figure 12. Figure 12(a) shows examples of multiple in-plane shapes of the film thickness on the substrate surface. As shown in Figure 12(a), each of the Zernike coefficients Z1 to Z11 corresponds to one of the multiple in-plane shapes of the film thickness on the substrate surface. For example, the Zernike coefficient Z4 corresponds to a convex in-plane shape. Also, the Zernike coefficient Z9 corresponds to a W-shaped in-plane shape.

[0054] FIG. 12(b) shows an example of the characteristics of a plurality of Zernike coefficients. The coordinates of the Zernike polynomial are in a polar coordinate system. As shown in FIG. 12(b), the Zernike coefficients Z1 to Z11 are associated with types, Zernike functions, and roles.

[0055] The Zernike polynomial is an orthogonal polynomial defined on the unit circle. In this embodiment, by linearly regressing the in-plane shape of the film thickness on the substrate surface predicted using the Zernike polynomial as a basis function, the characteristics of a plurality of in-plane shapes of the film thickness on the substrate surface can be extracted.

[0056] Also, in Equation (1), in order not to overfit even with a small number of measured film thickness data, as shown in FIG. 10, a normalization term is added for regression. As shown in Equation (1), the normalization coefficient λ i corresponds to the normalization term of each Zernike coefficient z i . In Equation (1), by reducing the normalization coefficient λ i of the important Zernike coefficient z i and increasing the normalization coefficient λ i of the other Zernike coefficients z i , it becomes possible to predict the film thickness with high accuracy while suppressing overfitting.

[0057] In this embodiment, by increasing the normalization coefficient λ4 of the Zernike coefficient Z4 associated with the convex in-plane shape and the normalization coefficient λ9 of the Zernike coefficient Z9 associated with the W-shaped in-plane shape, it is possible to predict the film thickness with high accuracy while suppressing overfitting.

[0058] The adjustment of the normalization coefficient λ i of the Zernike coefficient z i will be described while referring to FIG. 11. As shown in FIG. 11, by adjusting the normalization coefficient λ i of the Zernike coefficient z i according to the in-plane shape of the film thickness on the substrate surface, the prediction accuracy of the prediction model for predicting the film thickness on the substrate surface is improved. The adjustment of the normalization coefficient λ i of the Zernike coefficient z i is performed, for example, by an operator.

[0059] Figure 11(a) shows that when the in-plane shape of the film thickness on the substrate surface is eccentric, reducing the normalization coefficient λ2 of the Zernike coefficient Z2 and the normalization coefficient λ3 of the Zernike coefficient Z3 improves the prediction accuracy of the prediction model for predicting the film thickness on the substrate surface.

[0060] Furthermore, Figure 11(b) shows that when the in-plane shape of the film thickness on the substrate surface is not eccentric, increasing the normalization coefficient λ2 of the Zernike coefficient Z2 and the normalization coefficient λ3 of the Zernike coefficient Z3 improves the prediction accuracy of the prediction model for predicting the film thickness on the substrate surface.

[0061] Note that the Zernike coefficient z i λ, the normalization coefficient i This may be adjusted using cross-validation to minimize the mean squared error. Zernike coefficient z i λ, the normalization coefficient i For adjustment, methods such as leave-one-out cross-validation can be used. Also, the Zernike coefficient z i λ, the normalization coefficient i The adjustment may be performed for each substrate processing device 10 or for each process.

[0062] The process of regressing the measured film thickness data with the Zernike polynomial is illustrated, for example, in Figure 13. Figure 13(a) is an image diagram in which the film thickness on the substrate surface is represented by color, etc., based on the measured film thickness data (raw data). In step S12, the measured film thickness data shown in Figure 13(a) is used with the Zernike coefficient z shown in Figure 13(b). i An example of the quantified Zernike coefficients Z2 to Z11, shown in Figure 13(c), is obtained by regression with a Zernike polynomial having the following properties. As shown in Figure 13, the Zernike polynomial can quantitatively represent the in-plane shape pattern of the film thickness on the substrate surface.

[0063] Returning to step S14 in Figure 8, the prediction unit 56 of the device controller 12 predicts the film thickness data for multiple prediction points on the substrate surface using the prediction model created in step S12. The prediction unit 56 may, for example, predict the film thickness data for arbitrary coordinates (XY coordinates) on the substrate surface entered by the operator.

[0064] In step S16, the display control unit 60 displays the predicted film thickness data predicted by the prediction unit 56 in step S14 on an output device 502 such as a display. The format of the display of the predicted film thickness data is not limited; it may be displayed in a table format, or it may be displayed as an image diagram that shows the film thickness on the substrate surface in a way that can be identified by color, etc.

[0065] <Verification> The predictive model created in this embodiment was validated using film thickness data from 49 measurement points in past evaluation processes as validation data. The validation method is as follows.

[0066] Firstly, film thickness data for 13 measurement points is extracted from the validation data for 49 measurement points and input into the prediction model to predict the film thickness data for 49 prediction points (hereinafter referred to as the predicted values).

[0067] Secondly, film thickness data (hereinafter referred to as "true values") for 49 measurement points were extracted from the validation data for those 49 measurement points. Thirdly, the prediction accuracy of the prediction model was verified by comparing the 49 true values ​​with the predicted values.

[0068] Fourth, a comparison was made between the statistical values ​​of the in-plane film thickness of the substrate based on 49 true values ​​(average film thickness, range, or in-plane uniformity) and the statistical values ​​of the in-plane film thickness of the substrate based on 49 predicted values. The results of the comparison are shown, for example, in Figure 14.

[0069] Figure 14 is a graph showing an example of the results of a comparison between the statistical values ​​of the in-plane film thickness of the substrate based on 49 true values ​​and the statistical values ​​of the in-plane film thickness of the substrate based on 49 predicted values.

[0070] Figure 14(a) shows an example of the results of comparing the average film thickness among the statistical values ​​of the in-plane film thickness of the substrate with the predicted value. Figure 14(b) shows an example of the results of comparing the range among the statistical values ​​of the in-plane film thickness of the substrate with the predicted value. Figure 14(c) shows an example of the results of comparing the in-plane uniformity among the statistical values ​​of the in-plane film thickness of the substrate with the predicted value. As shown in Figures 14(a) to 14(c), the prediction model created in this embodiment is able to predict the statistical values ​​of the in-plane film thickness of the substrate with high accuracy.

[0071] This embodiment provides a technique for predicting film thickness data at multiple predicted points on the substrate surface with higher accuracy from measured film thickness data at a small number of measurement points. Furthermore, this embodiment allows for higher accuracy prediction of film thickness at any coordinate on the substrate surface without increasing the number of measurement points. For example, in this embodiment, it is possible to predict film thickness data for more measurement points (e.g., 49 points) than the number of measurement points in a mass production process from measured film thickness data at a small number of measurement points (e.g., 13 points) in a mass production process, thus enabling the calculation of statistical values ​​for in-plane film thickness with higher accuracy. Moreover, since this embodiment allows for the prediction of film thickness at any coordinate on the substrate surface, it is also possible to predict film thickness at locations that are important for quality control.

[0072] <Other Embodiments> For example, the film thickness prediction method according to this embodiment may be applied to a substrate processing apparatus that measures or estimates film thickness based on reflected light from a substrate. Substrate processing apparatuses that measure or estimate film thickness based on reflected light from a substrate are known, for example, as described in Japanese Patent Application Publication No. 2022-181680. For example, the substrate processing apparatus described in Japanese Patent Application Publication No. 2022-181680 is an example of a substrate processing apparatus having a measuring unit that measures measured film thickness data at a plurality of measurement points on the surface of a deposited substrate.

[0073] A substrate processing apparatus that measures or estimates film thickness based on reflected light from a substrate measures or estimates film thickness data at a small number of measurement points on the surface of the deposited substrate, and creates a predictive model by regression on the measured or estimated film thickness data using the Zernike polynomial. Using the created predictive model, the substrate processing apparatus can predict film thickness data for more than a small number of measurement points on the surface of the deposited substrate and output it as predicted film thickness data, which can then be displayed on the output device 502. Alternatively, the substrate processing apparatus may obtain measured film thickness data from the measurement device 11 by having a communication unit that receives measured film thickness data from multiple measurement points on the surface of the deposited substrate. The substrate processing apparatus that has obtained measured film thickness data from the measurement device 11 measures or estimates film thickness data at a small number of measurement points on the surface of the deposited substrate, and creates a predictive model by regression on the measured or estimated film thickness data using the Zernike polynomial. Then, using the created predictive model, the substrate processing apparatus predicts film thickness data for more than a small number of measurement points on the surface of the deposited substrate and outputs it as predicted film thickness data, which can then be displayed on the output device 502.

[0074] The embodiments disclosed herein should be considered in all respects to be illustrative and not restrictive. The embodiments described above may be omitted, replaced, or modified in various ways without departing from the scope and spirit of the appended claims. [Explanation of symbols]

[0075] 1. Film Thickness Prediction System 10 Substrate Processing Equipment 11 Measuring device 12. Device Controller 14 Server Devices 15 Database Devices 16. Worker terminal 50 Acquisition Department 52 Storage section 54 Predictive Model Creation Department 56 Prediction Section 58 Input Reception Section 60 Display Control Unit

Claims

1. An acquisition unit that acquires measurement film thickness data at multiple measurement points on the substrate surface formed by a substrate processing device, A prediction model creation unit creates a prediction model by regressing the measured film thickness data using the Zernike polynomial, A prediction unit that uses the prediction model to predict the film thickness data of multiple prediction points on the substrate surface and outputs it as predicted film thickness data, A display control unit that displays the predicted film thickness data on an output device, An information processing device having

2. The prediction model creation unit creates the prediction model by regression on the measured film thickness data using equation (1). The information processing apparatus according to claim 1. [Math 1] y: film thickness X: Design matrix z ｉ : Zernike coefficient λ ｉ : Normalization coefficient

3. The normalization coefficient λ of equation (1) ｉ This value is adjusted according to the in-plane shape of the film thickness on the substrate surface. The information processing apparatus according to claim 2.

4. The normalization coefficient λ of equation (1) ｉ This value is adjusted using cross-validation to minimize the mean squared error. The information processing apparatus according to claim 2.

5. An input receiving unit that receives input from an operator for multiple predicted points on the surface of the substrate, It further possesses, The prediction unit predicts the film thickness data of a plurality of prediction points on the substrate surface that have received the input. The information processing apparatus according to claim 1.

6. The display control unit displays the in-plane distribution of the film thickness on the substrate surface. The information processing apparatus according to claim 1.

7. The prediction model creation unit creates a prediction model by regressing the measured film thickness data of a number of measurement points smaller than the number of prediction points on the substrate surface using the Zernike polynomial. The information processing apparatus according to any one of claims 1 to 6.

8. A substrate processing apparatus for forming a film on the surface of a substrate, A communication unit that receives measurement film thickness data from multiple measurement points on the surface of a deposited substrate, A prediction model creation unit creates a prediction model by regressing the measured film thickness data using the Zernike polynomial, A prediction unit that uses the prediction model to predict the film thickness data of multiple prediction points on the substrate surface and outputs it as predicted film thickness data, A display control unit that displays the predicted film thickness data on an output device, A substrate processing apparatus having

9. A measurement unit that measures the film thickness data at multiple measurement points on the surface of a deposited substrate. The substrate processing apparatus according to claim 8, further comprising the above.

10. A method for predicting film thickness performed by an information processing device, To acquire measurement film thickness data at multiple measurement points on the substrate surface deposited by a substrate processing device, The aforementioned measured film thickness data is regressed using the Zernike polynomial to create a predictive model, Using the prediction model, the thickness data of multiple prediction points on the substrate surface is predicted and output as predicted thickness data. The predicted film thickness data is displayed on the output device, A method for predicting film thickness, comprising the characteristics of a film thickness prediction method.

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