Inference model creation device, inference model creation method, and storage medium

Abstract

In the present invention, a color change inference model creation unit determines, on the basis of a prior-to-processing image newly acquired by a prior-to-processing image acquisition unit and a reference value calculated by a reference value calculation unit, whether or not a color change inference model should be updated. When it is determined that the color change inference model should be updated, the color change inference model creation unit uses the newly acquired prior-to-processing image to update the color change inference model.

Description

Estimation Model Creation Device, Estimation Model Creation Method, and Storage Medium

[0001] The present disclosure relates to an estimation model creation device, an estimation model creation method, and a storage medium.

[0002] Patent Document 1 discloses an estimation model creation device related to a shape characteristic value estimation model for estimating a shape characteristic value, which is a characteristic value related to the shape of a target film subjected to film processing on a substrate.

[0003] Japanese Patent No. 7482018

[0004] The present disclosure provides a technique capable of more easily creating and updating a model for estimating a characteristic value related to the shape of a substrate.

[0005] An estimation model creation device according to an aspect of the present disclosure is an estimation model creation device related to a shape characteristic value estimation model for estimating a shape characteristic value, which is a characteristic value related to the shape of a target film subjected to film processing on a substrate. The estimation model creation device includes a post - processing image acquisition unit that acquires a post - processing image, which is image information related to the surface of the substrate after the film processing, and a pre - processing image acquisition unit that acquires a pre - processing image, which is image information related to the surface of the substrate before the film processing. The estimation model creation device includes a color change estimation model creation unit that creates a color change estimation model for estimating information related to the color of the surface of the substrate included in the post - processing image from information related to the color of the surface of the substrate included in the pre - processing image. The estimation model creation device includes a reference value calculation unit that calculates a reference value for updating the color change estimation model based on the pre - processing images of the plurality of substrates for learning. The estimation model creation device includes a correlation estimation model creation unit that obtains a difference between information related to the color of the surface of the substrate included in the post - processing image and a result estimated by the color change estimation model, and creates a correlation estimation model for estimating a correlation between the difference and the shape characteristic value of the target film subjected to the film processing. The color change estimation model creation unit determines whether to update the color change estimation model based on the newly acquired pre - processing image by the pre - processing image acquisition unit and the reference value calculated by the reference value calculation unit. When it is determined that the update should be performed, the color change estimation model creation unit updates the color change estimation model using the newly acquired pre - processing image.

[0006] This disclosure provides a technology that makes it easier to create and update models for estimating characteristic values ​​related to the shape of a substrate.

[0007] Figure 1 is a schematic diagram showing an example of the general configuration of a substrate processing system. Figure 2 is a schematic diagram showing an example of a coating and developing apparatus. Figure 3 is a schematic diagram showing an example of an inspection unit. Figure 4 is a block diagram showing an example of the functional configuration of a control device. Figure 5 schematically shows the changes in color-related information obtained from image data of multiple wafers. Figure 6 is a diagram illustrating the challenges in CD estimation. Figure 7 is a diagram illustrating additional learning. Figure 8 is a diagram illustrating the creation of a CD estimation model. Figure 9 is a block diagram showing an example of the hardware configuration of a control device. Figure 10 is a diagram showing an example of the apparatus configuration. Figure 11 is a diagram showing an example of the apparatus configuration. Figure 12 is a flowchart showing an example of the additional learning process.

[0008] Various exemplary embodiments will be described in detail below with reference to the drawings. In each drawing, the same or corresponding parts will be denoted by the same reference numerals.

[0009] [Substrate Processing System] The substrate processing system 1 is a system that performs the following on a workpiece W: formation of a photosensitive film, exposure of the photosensitive film, and development of the photosensitive film. The workpiece W to be processed is, for example, a substrate, or a substrate in which a film or circuit has been formed by a predetermined process. One example of a substrate included in the workpiece W is a silicon wafer. The workpiece W (substrate) may be formed in a circular shape. The workpiece W to be processed may be a glass substrate, a mask substrate, an FPD (Flat Panel Display), etc., or an intermediate obtained by performing a predetermined process on these substrates, etc. The photosensitive film is, for example, a resist film.

[0010] The substrate processing system 1 comprises a coating / developing apparatus 2 and an exposure apparatus 3. The exposure apparatus 3 performs exposure processing on a resist film (photosensitive coating) formed on a workpiece W (substrate). Specifically, the exposure apparatus 3 irradiates the portion of the resist film to be exposed with energy rays using methods such as immersion exposure. The coating / developing apparatus 2 performs a process to form a resist film on the surface of the workpiece W before exposure processing by the exposure apparatus 3, and performs development processing on the resist film after exposure processing.

[0011] [Substrate Processing Apparatus] The following describes the configuration of a coating / developing apparatus 2 as an example of a substrate processing apparatus. As shown in Figures 1 and 2, the coating / developing apparatus 2 comprises a carrier block 4, a processing block 5, an interface block 6, and a control device 100 (control unit). The coating / developing apparatus 2 as a substrate processing apparatus described in this embodiment corresponds to a shape characteristic value estimation device that estimates shape characteristic values ​​related to the shape of a target film formed on a substrate, and an estimation model creation device used for estimating shape characteristic values. In this embodiment, the "shape characteristic value" related to the shape of the target film corresponds to a feature quantity related to the shape of the target film. As an example, the shape characteristic value is line width (CD: Critical Dimension). Note that the shape characteristic value may also be the film thickness of the target film. In the following embodiment, the case in which the coating / developing apparatus 2 estimates the CD of the target film as a shape characteristic value estimation device will be described. The function of the coating / developing apparatus 2 for estimating CD will be described later.

[0012] The carrier block 4 introduces the workpiece W into the coating / developing apparatus 2 and takes the workpiece W out of the coating / developing apparatus 2. For example, the carrier block 4 can support multiple carriers C (storage sections) for the workpiece W and incorporates a transport device A1 including a transfer arm. The carrier C accommodates, for example, multiple circular workpieces W. The transport device A1 takes the workpiece W from the carrier C and passes it to the processing block 5, and receives the workpiece W from the processing block 5 and returns it to the carrier C. The processing block 5 has multiple processing modules 11, 12, 13, and 14.

[0013] The processing module 11 incorporates a plurality of coating units U1, a plurality of heat treatment units U2, a plurality of inspection units U3, and a transport device A3 for transporting workpieces W to these units. The processing module 11 forms an underlayer film on the surface of the workpiece W using the coating units U1 and the heat treatment units U2. The coating unit U1 of the processing module 11 applies a processing liquid for underlayer film formation onto the workpiece W while rotating the workpiece W at a predetermined rotational speed. The heat treatment unit U2 of the processing module 11 performs various heat treatments associated with the formation of the underlayer film. The heat treatment unit U2 incorporates, for example, a hot plate and a cooling plate, and heats the workpiece W to a predetermined heating temperature using the hot plate, and then cools the heated workpiece W using the cooling plate to perform the heat treatment. The inspection unit U3 performs processing to inspect the surface condition of the workpiece W and acquires information indicating the surface condition of the workpiece W, such as a surface image or information related to shape characteristic values ​​(CD).

[0014] The processing module 12 incorporates a plurality of coating units U1, a plurality of heat treatment units U2, a plurality of inspection units U3, and a transport device A3 for transporting workpieces W to these units. The processing module 12 forms an intermediate film on the underlying film using the coating units U1 and the heat treatment units U2. The coating unit U1 of the processing module 12 forms a coating film on the surface of the workpiece W by applying a processing liquid for intermediate film formation onto the underlying film. The heat treatment unit U2 of the processing module 12 performs various heat treatments associated with the formation of the intermediate film. The heat treatment unit U2 incorporates, for example, a hot plate and a cooling plate, and heats the workpiece W to a predetermined heating temperature using the hot plate, and then cools the heated workpiece W using the cooling plate to perform the heat treatment. The inspection unit U3 performs processing to inspect the surface condition of the workpiece W and acquires information indicating the surface condition of the workpiece W, such as a surface image or information related to shape characteristic values ​​(CD).

[0015] The processing module 13 incorporates a plurality of coating units U1, a plurality of heat treatment units U2, a plurality of inspection units U3, and a transport device A3 for transporting workpieces W to these units. The processing module 13 forms a resist film on an intermediate film using the coating units U1 and the heat treatment units U2. The coating unit U1 of the processing module 13 applies a processing liquid for resist film formation onto the intermediate film while rotating the workpiece W at a predetermined rotational speed. The heat treatment unit U2 of the processing module 13 performs various heat treatments associated with the formation of the resist film. The heat treatment unit U2 of the processing module 13 forms a resist film by applying heat treatment (PAB: Post Applied Bake) to the workpiece W on which the coating film has been formed at a predetermined heating temperature. The inspection unit U3 performs processing to inspect the surface condition of the workpiece W and acquires information indicating the surface condition of the workpiece W, such as information related to shape characteristic values ​​(CD).

[0016] The processing module 14 incorporates a plurality of coating units U1, a plurality of heat treatment units U2, and a transport device A3 for transporting workpieces W to these units. The processing module 14 performs development processing of the resist film R after exposure using the coating units U1 and the heat treatment units U2. The coating unit U1 of the processing module 14 performs development processing of the resist film R by, for example, applying a developer solution to the surface of the exposed workpiece W while rotating the workpiece W at a predetermined rotation speed, and then washing it off with a rinsing solution. The heat treatment unit U2 of the processing module 14 performs various heat treatments associated with the development process. Specific examples of heat treatments include heat treatment before development (PEB: Post Exposure Bake) and heat treatment after development (PB: Post Bake).

[0017] A shelf unit U10 is provided on the carrier block 4 side within the processing block 5. The shelf unit U10 is divided into multiple cells arranged vertically. A transport device A7, including a lifting arm, is provided near the shelf unit U10. The transport device A7 lifts and lowers the workpiece W between the cells of the shelf unit U10.

[0018] A shelf unit U11 is provided on the interface block 6 side within the processing block 5. The shelf unit U11 is divided into multiple cells arranged in the vertical direction.

[0019] The interface block 6 handles the transfer of workpieces W to and from the exposure device 3. For example, the interface block 6 incorporates a transport device A8, which includes a transfer arm, and is connected to the exposure device 3. The transport device A8 transfers the workpieces W placed on the shelf unit U11 to the exposure device 3, and receives the workpieces W from the exposure device 3 and returns them to the shelf unit U11.

[0020] [Inspection Unit] The inspection unit U3 included in processing modules 11 to 13 will now be described. The inspection unit U3 has the function of imaging the surface of a film (e.g., a base layer, an intermediate layer, a resist film, etc.) formed by the coating unit U1 and the heat treatment unit U2, and obtaining image data.

[0021] As shown in Figure 3, the inspection unit U3 includes a housing 30, a holding unit 31, a linear drive unit 32, an imaging unit 33, and a light-emitting / reflecting unit 34. The holding unit 31 holds the workpiece W horizontally. The linear drive unit 32 uses, for example, an electric motor as a power source to move the holding unit 31 along a horizontal, straight path. The imaging unit 33 has a camera 35, such as a CCD camera. The camera 35 is located at one end of the inspection unit U3 in the direction of movement of the holding unit 31 and is directed toward the other end in that direction of movement. The light-emitting / reflecting unit 34 emits light into the imaging range and guides the reflected light from the imaging range toward the camera 35. For example, the light-emitting / reflecting unit 34 has a half mirror 36 and a light source 37. The half mirror 36 is located at a position higher than the holding unit 31 and in the middle of the movement range of the linear drive unit 32, and reflects light from below toward the camera 35. The light source 37 is mounted on the half mirror 36 and illuminates downwards through the half mirror 36.

[0022] The inspection unit U3 operates as follows to acquire image data of the surface of the workpiece W. First, the linear drive unit 32 moves the holding unit 31. This causes the workpiece W to pass under the half mirror 36. During this passage process, reflected light from various parts of the surface of the workpiece W is sequentially sent to the camera 35. The camera 35 forms an image of the reflected light from various parts of the surface of the workpiece W and acquires image data of the surface of the workpiece W. When the shape of the film formed on the surface of the workpiece W (for example, a CD) changes, the image data of the surface of the workpiece W captured by the camera 35 changes, for example, the color of the surface of the workpiece W changes in accordance with the change in shape. In other words, acquiring image data of the surface of the workpiece W is equivalent to acquiring information related to the shape of the film formed on the surface of the workpiece W. This point will be described later.

[0023] Image data acquired by camera 35 is sent to control device 100. The control device 100 can estimate the shape characteristic values ​​of the film on the surface of the workpiece W based on the image data, and the estimation results are stored in the control device 100 as inspection results. The image data is also stored in the control device 100.

[0024] [Control Device] An example of the control device 100 will be described in detail. The control device 100 controls each element included in the coating and developing apparatus 2. The control device 100 is configured to perform process operations including forming the above-mentioned films on the surface of the workpiece W and performing a developing process. Furthermore, as the main part of the shape characteristic value estimation device, the control device 100 is configured to perform processing for estimating the shape characteristic values ​​of the formed film. Here, an example of the configuration of the control device 100 when estimating the CD of the target film as a shape characteristic value in the coating and developing apparatus 2 will be described.

[0025] As shown in Figure 4, the control device 100 includes a background image acquisition unit 101 (pre-processing image acquisition unit), a post-processing image acquisition unit 102, an image information holding unit 103, a model creation unit 104, an estimated model holding unit 105, an estimation unit 106, and a reference value calculation unit 107. Each part of the control device 100 is shown as an example of its functional configuration. The model creation unit 104 includes a gray value estimation model creation unit 111 and a CD estimation model creation unit 112. Each functional unit shown in Figure 4 is a functional unit for realizing the function of a CD estimation device, which is a type of shape characteristic value estimation device. Furthermore, each functional unit shown in Figure 4 also includes a functional unit for realizing the function of a CD estimation model creation device, which is a type of shape characteristic value estimation model creation device.

[0026] Before describing each functional unit, an overview of the processing (inspection) performed by the coating and developing apparatus 2, including the control device 100, as an apparatus for inspecting substrates will be explained. The coating and developing apparatus 2 performs a process of estimating the CD of the film formed on the surface of the workpiece W from an image of the workpiece W's surface. When the film on the surface of the workpiece W is developed, the color of the surface changes due to its CD. Utilizing this, the coating and developing apparatus 2 estimates the CD at each point on the surface of the workpiece W from image data that includes information related to the color of the workpiece W's surface.

[0027] The general procedure for estimating CD is as follows: First, prepare several workpieces for which the CD of the target film (the film to be estimated) is known. Then, create a model relating the color information of each pixel in the image data of the surface of these workpieces to the CD of the film on the wafer surface at the position captured by that pixel. Subsequently, acquire an image of the surface of a workpiece on which the target film to be CD estimated is formed, and estimate the CD of the film on the workpiece surface based on the color information of each pixel contained in the image data and the correlation model described above. This allows for the estimation of the CD of the target film on the workpiece surface.

[0028] Figure 5 schematically shows the changes in color information obtained from image data of multiple workpieces. In Figure 5, the surface color information (here, gray value) obtained from image data of the workpiece surface after the target film has been developed is shown. As shown in Figure 5, each workpiece shows a different color from the others, so the CD of the film on the workpiece surface is estimated using this difference in color.

[0029] However, the above method may not create a model that takes into account the conditions of the underlying layers of the film for which CD estimation is being attempted. As mentioned above, multiple films are formed on a workpiece. For example, if the film for which CD estimation is attempted is a resist film, there may be underlying and intermediate films stacked beneath the resist film, and there may be films formed in other processes beneath the underlying film. Therefore, the differences in the color of the workpiece surface for each workpiece, as shown in Figure 5, may not be due to changes in the CD of the film for which CD estimation is attempted, but rather reflect variations in the state of the underlying layers. Thus, it is quite possible that variations in the state of the underlying layers are reflected in variations in the color changes of the workpiece surface.

[0030] The CD estimation model described above estimates the correlation between the CD of the resist film and the color information in the image data, but it does not take into account cases where the conditions of each film below the resist film are different. For example, if the thickness of the interlayer film below the resist film changes, the color of the workpiece surface may change even before the resist film is applied due to the thickness of the interlayer film. However, the CD estimation model may not adequately reflect the influence of such underlying films. Considering the above problems, one option would be to create a CD estimation model using workpieces with varying conditions (thickness, etc.) of the underlying films. However, it is possible that it may be difficult to prepare a considerable number of workpieces that correspond to the various conditions necessary to create a model with high estimation accuracy.

[0031] In the coating and developing apparatus 2 described in this embodiment, a color change estimation model is created from image information (underlying image: pre-processing image) of the surface of the workpiece W below the target film, which is the base layer, to estimate how the color of the surface of the workpiece W will change after the target film is formed. Here, a gray value estimation model is created to estimate the change in gray value. Then, assuming that the difference between the measured gray value and the estimated gray value obtained by applying the gray value estimation model to the underlying image correlates with CD, a CD estimation model is created that shows the correlation between the above difference and CD. In the coating and developing apparatus 2 described in this embodiment, a more accurate CD estimation result is achieved by estimating CD using these two models as the CD estimation model used for CD estimation. Details of these two models will be described later.

[0032] Figure 6 illustrates the challenges in CD estimation. In Figure 6, the horizontal axis represents time, and the vertical axis represents the CD estimation error (|measured value - estimated value| / measured value). Each bar graph shows the results for each work W. Up to time t1, the results for the training work W (training sample) are shown. If we consider time t1 to t2 as the first half and time t2 onwards as the second half, it can be seen that the CD estimation error clearly increases in the second half, indicating a deterioration in CD estimation accuracy. Possible factors include the appearance of background samples with colors that were not present during training. Thus, because the conditions of the background of work W may change, the CD estimation accuracy may deteriorate over time.

[0033] To address these challenges, for example, as shown in Figure 7(a), if training is performed using all data (training samples used when creating the estimation model and work W for the period including new fluctuating factors), a massive amount of storage is required to accumulate all the data. In addition, the amount of computation required for training becomes large. This leads to problems such as high costs and long training times. In this regard, for example, as shown in Figure 7(b), consider the case where the existing estimation model (the model currently in operation) is used, and only the data from work W for the period including new fluctuating factors is additionally trained. In this case, the accumulation of training data can be reduced (saves storage capacity), and the amount of computation required for training can be reduced, thereby achieving low costs and shorter training times. In this embodiment, we will explain the process assuming that such additional training is performed.

[0034] Returning to Figure 4, the base image acquisition unit 101 has the function of acquiring image information (base image: sometimes called a pre-processing image) of the surface of the workpiece W that will form the target film for CD estimation before the target film is developed (before film processing). The base image acquisition unit 101 acquires the base image of the target workpiece W by, for example, controlling the inspection unit U3.

[0035] The post-processing image acquisition unit 102 has the function of acquiring image information (post-processing image) of the surface of the workpiece W (film-treated workpiece W) after the target film has been developed. The post-processing image acquisition unit 102 acquires the post-processing image of the target workpiece W by, for example, controlling the inspection unit U3.

[0036] The image information holding unit 103 has the function of holding the background image acquired by the background image acquisition unit 101 and the processed image acquired by the processed image acquisition unit 102. The image information held by the image information holding unit 103 is used in estimating the CD of the target film formed on the workpiece W.

[0037] The model creation unit 104 has the function of creating a CD estimation model used to estimate the CD of the target film formed on the workpiece W. As will be described in detail later, the CD estimation model created by the model creation unit 104 includes a Gray value estimation model and a CD estimation model. The Gray value estimation model creation unit 111 of the model creation unit 104 has the function of creating a Gray value estimation model, and the CD estimation model creation unit 112 has the function of creating a CD estimation model.

[0038] The gray value estimation model creation unit 111 learns information (gray value) related to the surface color of work W included in the background image and information (gray value) related to the surface color of work W included in the processed image for each of the multiple work W (training samples) used for training. Through this learning, the gray value estimation model creation unit 111 creates a gray value estimation model that estimates the gray value of work W included in the processed image from the gray value of work W included in the background image. Alternatively, the gray value estimation model creation unit 111 may also create a gray value estimation model that estimates the gray value of work W included in the background image through the above learning. In this case, the gray value estimation model is represented by the estimation models in equations (1) and (2) below. X is the estimated value of the gray value of work W included in the background image, Y is the estimated value of the gray value of work W included in the processed image, and x is the measured value of the gray value of work W included in the background image. X = A(x) ... (1) Y = B(x) ... (2)

[0039] The grayscale value estimation model creation unit 111 calculates the estimation error Δx, which is the difference between the measured value and the estimated value in the background image, based on the grayscale value estimation model, for each of the multiple workpieces W (training samples) used for training. Specifically, the grayscale value estimation model creation unit 111 calculates the estimation error Δx for each training sample, which is the difference between the measured value of the grayscale in the background image and the estimated value of the grayscale estimated by the grayscale value estimation model. The grayscale value estimation model creation unit 111 calculates the estimation error Δy, which is the difference between the measured value and the estimated value in the processed image, based on the grayscale value estimation model, for each of the multiple workpieces W (training samples) used for training. Specifically, the grayscale value estimation model creation unit 111 calculates the estimation error Δy for each training sample, which is the difference between the measured value of the grayscale in the processed image and the estimated value of the grayscale estimated by the grayscale value estimation model.

[0040] The reference value calculation unit 107 calculates a reference value for updating the grayscale estimation model (to determine whether or not to update it) based on the background images of multiple workpieces W (training samples) for training. The reference value calculation unit 107 may also calculate a summary amount of the estimation error Δx, which is the difference between the measured grayscale value in the background image and the estimated grayscale value estimated by the grayscale estimation model for each of the multiple workpieces W (training samples) for training, and use this summary amount as the reference value. Here, the summary amount may be, for example, 3σ, where σ is the standard deviation of the absolute value of the estimation error Δx for each training sample.

[0041] The grayscale value estimation model creation unit 111 determines whether or not to update the grayscale value estimation model based on the multiple background images newly acquired by the background image acquisition unit 101 and the reference value calculated by the reference value calculation unit 107. If the grayscale value estimation model creation unit 111 determines that it should be updated, it updates the grayscale value estimation model using the newly acquired background images. The grayscale value estimation model creation unit 111 may also determine that the grayscale value estimation model should be updated if the summation amount of the estimation error Δx' of the multiple background images newly acquired by the background image acquisition unit 101 is greater than or equal to a predetermined value compared with the reference value calculated by the reference value calculation unit 107. Updating the grayscale value estimation model means performing additional learning. The newly acquired background images here are not background images of training samples, but background images acquired after the creation of the grayscale value estimation model (for example, at the estimation stage). The summation amount of the estimation error Δx' of the multiple background images newly acquired may be, for example, 3σ, where σ is the standard deviation of the estimation error Δx' of the multiple background images newly acquired. In this case, the gray value estimation model creation unit 111 may determine that the gray value estimation model should be updated if the 3σ of Δx' of the newly acquired multiple background images is greater than or equal to a predetermined value by a predetermined multiple of the 3σ of the estimation error Δx (reference value) of each training sample. Here, the predetermined value or greater may be, for example, around 1 to 3 times.

[0042] The gray value estimation model creation unit 111 may further create a difference prediction model that predicts the estimation errors Δx' and Δy' when the summation amount of the estimation error Δx' of the newly acquired multiple background images is greater than or equal to a predetermined value compared to a reference value. The difference prediction models Δxp and Δyp are shown, for example, by the following equations (3) and (4): Δxp = C(x) ... (3) Δyp = D(x) ... (4)

[0043] The gray value estimation model creation unit 111 may update the gray value estimation model using the difference prediction model. Since the difference prediction model predicts how much the actual gray value deviates from the existing gray value estimation model, the new gray value estimation model is represented by the following equations (5) and (6). Xnew is the estimated value of the gray value of the work W included in the base image, and Ynew is the estimated value of the gray value of the work W included in the processed image. Xnew = X + Δxp = A(x) + C(x) = A´(x) ··· (5) Ynew = Y + Δyp = B(x) + D(x) = B´(x) ··· (6)

[0044] When the summary amount of the estimation error Δx´ of a plurality of newly acquired base images is larger than a predetermined value multiple compared to the reference value, the gray value estimation model creation unit 111 may further create a difference prediction model that predicts the estimation error Δy´ based on the estimation error Δx´. The difference prediction models Δxp and Δyp in this case are represented by, for example, the following equations (7) and (8). Δxp = E(Δx´) ··· (7) Δyp = F(Δx´) ··· (8)

[0045] The gray value estimation model creation unit 111 may update the gray value estimation model using the difference prediction model. Since the difference prediction model predicts how much the actual gray value deviates from the existing gray value estimation model, the new gray value estimation model is represented by the following equations (9) and (10). Xnew = X + Δxp = A(x) + E(Δx´) = A(x) + E(x - X) = A(x) + E(x - A(x)) = A´´(x) ··· (9) Ynew = Y + ΔYp = B(x) + F(Δx´) = B(x) + F(x - X) = B(x) + F(x - B(x)) = B´´(x) ··· (10)

[0046] In the learning stage, the gray value estimation model creation unit 111 may exclude (outlier exclusion) the work W (learning sample) in which at least one of the estimation error Δx and the estimation error Δy is larger than a predetermined value from the learning samples.

[0047] The above process for excluding abnormal values is as follows. First, a gray value estimation model is constructed by learning the gray values of the learning samples. Subsequently, for each learning sample, estimation errors Δx and Δy are derived, and their absolute values are calculated by the following equations (11) and (12). ||Δx|| = (Δx1^2 + Δx2^2 + … + Δxn^2)^0.5 … (11) ||Δy|| = (Δy1^2 + Δy2^2 + … + Δyn^2)^0.5 … (12)

[0048] Then, 3σ(||Δx||) and 3σ(||Δy||) among all the learning samples are derived. If a learning sample with ||Δx|| > 3σ(||Δx||) or ||Δy|| > 3σ(||Δy||) is included in all the learning samples, the corresponding learning sample is excluded. And the constructed gray value estimation model is discarded, and the construction of the gray value estimation model is performed again. Also, if no learning sample with ||Δx|| > 3σ(||Δx||) or ||Δy|| > 3σ(||Δy||) is included, the final estimation model (the above equations (1) and (2)) and 3σ(||Δx||) are saved, and the reference value calculation by the reference value calculation unit 107 is performed.

[0049] In the stage of updating (additional learning) the gray value estimation model, the gray value estimation model creation unit 111 may exclude (exclude abnormal values) a workpiece W in which at least one of the estimation errors Δxnew and Δynew is greater than a predetermined value from the additional learning samples.

[0050] The above process for excluding abnormal values is as follows. First, an updated gray value estimation model is constructed by additional learning (the above equations (5) and (6), or equations (9) and (10), etc.). Subsequently, based on the updated gray value estimation model, an estimation error Δxnew, which is the difference between the measured value and the estimated value in the base image, is calculated, and an estimation error Δynew, which is the difference between the measured value and the estimated value in the processed image, is calculated. Then, for each sample, ||Δxnew|| and ||Δynew|| are derived, and 3σ(||Δxnew||) and 3σ(||Δynew||) among all the samples are derived.

[0051] If any sample contains a value where ||Δxnew|| > 3σ (||Δxnew||) or ||Δynew|| > 3σ (||Δynew||), that sample is excluded. The constructed Gray value estimation model is then discarded, and the Gray value estimation model is reconstructed. If no sample contains a value where ||Δxnew|| > 3σ (||Δxnew||) or ||Δynew|| > 3σ (||Δynew||), the final estimation model and 3σ (||Δxnew||) are saved, and the reference value calculation unit 107 performs the reference value calculation. In this way, if there is a sample in which at least one of the estimation error Δxnew and the estimation error Δynew is greater than a predetermined value, the Gray value estimation model creation unit 111 discards the updated Gray value estimation model and creates the Gray value estimation model again.

[0052] The Gray value estimation model creation unit 111 may create a Gray value estimation model for each workpiece W (wafer), or it may create one more finely for each exposure shot. Alternatively, the Gray value estimation model creation unit 111 may acquire Gray values ​​for each exposure shot, average the Gray values ​​for training for each workpiece W, and create a Gray value estimation model for each workpiece W. In this case, the Gray value residual for CD estimation will be the value for each exposure shot, but for additional training, the Gray value residual may be averaged for each workpiece W and accumulated.

[0053] The CD estimation model creation unit 112 calculates the estimation error Δy, which is the difference between the measured gray value of the workpiece W included in the processed image and the result estimated by the gray value estimation model. The CD estimation model creation unit 112 then creates a CD estimation model (CD estimation model) that estimates the correlation between the estimation error Δy and the shape characteristic value (CD) of the film-treated target film.

[0054] Figure 8 illustrates the creation of a CD estimation model. In Figure 8(a), the horizontal axis represents the estimated value Y of the grayscale value of workpiece W contained in the processed image, estimated by equation (2) (Y = B(x)) described above, and the vertical axis represents the measured value of the grayscale value of workpiece W contained in the processed image. In the example in Figure 8(a), the estimation error Δy, which is the difference between the measured value and the estimated value of the grayscale value, is calculated for each of the four samples (Sample A to Sample D). In Figure 8(b), the horizontal axis represents the estimation error Δy, and the vertical axis represents the measured value of CD. For example, a general regression method can be used to obtain the CD estimation model shown in equation (13) below: CD = f(Δy) ... (13)

[0055] The CD estimation model creation unit 112 may create a CD estimation model for each workpiece W (wafer), or it may create one more finely for each exposure shot.

[0056] The estimation model holding unit 105 has the function of holding the CD estimation model created by the model creation unit 104 (specifically, the CD estimation model creation unit 112).

[0057] The estimation unit 106 has the function of estimating the CD of the target film based on the background image and the processed image held in the image information holding unit 103. A CD estimation model is used for the CD estimation by the estimation unit 106.

[0058] The control device 100 is composed of one or more control computers. For example, the control device 100 has the circuit 120 shown in Figure 9. The circuit 120 has one or more processors 121, a memory 122, a storage 123, and an input / output port 124. The storage 123 has a storage medium that can be read by the computer, such as a hard disk. The storage medium stores a program that causes the control device 100 to execute the substrate inspection procedure described later. The storage medium may be a removable medium such as a non-volatile semiconductor memory, magnetic disk, or optical disk. The memory 122 temporarily stores the program loaded from the storage medium of the storage 123 and the calculation results by the processor 121. The processor 121 executes the above program in cooperation with the memory 122 to constitute each of the above-described functional modules. The input / output port 124 inputs and outputs electrical signals to and from the controlled component according to commands from the processor 121.

[0059] Furthermore, the hardware configuration of the control device 100 is not necessarily limited to configuring each functional module by program. For example, each functional module of the control device 100 may be composed of a dedicated logic circuit or an ASIC (Application Specific Integrated Circuit) that integrates such circuits.

[0060] In the following embodiments, the above configuration is described in the case where it is included in the control device 100, but the control device 100 does not have to include all of the above functions. For example, as shown in Figure 10, the coating and developing apparatus 2 may be configured to include a control device 100A (device) and a data server 200 (server). The control device 100A may be equipped with functions such as a base image acquisition unit 101 and a post-processing image acquisition unit 102, as well as functions related to gray value estimation and CD estimation, and the data server 200 may be equipped with functions for managing gray value estimation models and CD estimation models and recipe management. Also, as shown in Figure 11, the coating and developing apparatus 2 may be configured to include control devices 100B, 100C (devices) and a data server 200A (server). In this case, the control device 100B may be equipped with the function of a post-processing image acquisition unit 102, and the control device 100C may be equipped with the function of a base image acquisition unit 101. Furthermore, the data server 200A may be equipped with functions for managing the gray value estimation model and the CD estimation model, recipe management, and functions related to gray value estimation and CD estimation. As described above, the coating and developing apparatus 2 may be configured to include one or more devices, at least a post-processing image acquisition unit 102 and a base image acquisition unit 101, and a server provided separately from the apparatus, which holds at least each estimation model.

[0061] Next, the additional training process for the Gray value estimation model will be explained with reference to Figure 12. Figure 12 is a flowchart showing an example of the additional training process.

[0062] As shown in Figure 12, first, a grayscale estimation model is created (Step S1). Next, a reference value is calculated and saved to determine whether or not to update the grayscale estimation model based on the background image of the workpiece W used as a training sample (Step S2). Subsequently, the difference between the measured grayscale value of the workpiece W contained in the processed image and the result estimated by the grayscale estimation model is calculated, and a CD estimation model is created to estimate the correlation between this difference and CD (Step S3).

[0063] Next, sample preparation and estimation data accumulation are performed (step S4). Outdated data is deleted as needed (step S5). Then, it is determined whether the variability of the accumulated estimation data (the summary amount of the estimation error Δx of the newly acquired multiple background images) is greater than or equal to a predetermined value compared to a reference value (step S6). If it is not greater, the process is repeated from step S4; if it is greater, additional learning related to updating the gray value estimation model is performed (step S7), and the process is repeated from step S2.

[0064] Next, we will explain the operation and effects of the coating and developing apparatus 2 (estimated model creation apparatus).

[0065] The coating and developing apparatus 2 is an estimation model creation apparatus related to a shape characteristic value estimation model that estimates shape characteristic values, which are characteristic values ​​relating to the shape of a target film that has been film-treated on a workpiece W. The coating and developing apparatus 2 includes a post-processing image acquisition unit 102 that acquires a post-processing image, which is image information relating to the surface of the film-treated workpiece W, and a base image acquisition unit 101 that acquires a base image, which is image information relating to the surface of the workpiece W before film treatment. The coating and developing apparatus 2 includes a gray value estimation model creation unit 111 that creates a gray value estimation model by learning the gray values ​​contained in the base image and the gray values ​​contained in the post-processing image for each of a plurality of workpieces W for learning. The coating and developing apparatus 2 includes a reference value calculation unit 107 that calculates a reference value for updating the gray value estimation model based on the base images of the plurality of workpieces W for learning. The coating and developing apparatus 2 includes a CD estimation model creation unit 112 that calculates the difference between the measured gray value of the workpiece W included in the processed image and the result estimated by the gray value estimation model, and creates a CD estimation model that estimates the correlation between this difference and the CD of the target film that has been film-treated. The gray value estimation model creation unit 111 determines whether or not to update the gray value estimation model based on the background image newly acquired by the background image acquisition unit 101 and the reference value calculated by the reference value calculation unit 107. If the gray value estimation model creation unit 111 determines that it should be updated, it updates the gray value estimation model using the newly acquired background image and the processed image.

[0066] With this configuration, for example, a newly acquired background image is compared with a reference value created based on the grayscale value estimation model, and it can be determined that the grayscale value estimation model should be updated when the background conditions change. By updating the grayscale value estimation model using the newly acquired background image and the processed image, the accumulation of training data can be reduced, and the computational load for training can be reduced, compared to, for example, when training is performed again using all the data. In other words, it is possible to achieve lower costs and shorter training times for updating the grayscale value estimation model. This provides a technology that makes it easier to create and update models for estimating characteristic values ​​related to the shape of the workpiece W.

[0067] The gray value estimation model creation unit 111 may create a gray value estimation model that further estimates information related to the surface color of the workpiece W included in the background image. The gray value estimation model creation unit 111 may calculate an estimation error Δx, which is the difference between the measured value and the estimated value in the background image, based on the gray value estimation model, for each of the multiple workpieces used for training. The gray value estimation model creation unit 111 may also calculate an estimation error Δy, which is the difference between the measured value and the estimated value in the processed image, for each of the multiple workpieces used for training. By calculating the estimation errors Δx and Δy in this way, the variability of the estimated values ​​can be appropriately derived, and it is possible to appropriately detect the occurrence of background samples with colors that were not present during training.

[0068] The reference value calculation unit 107 may calculate a summary amount of the estimation error Δx for each of the multiple learning workpieces W, and use this summary amount as the reference value. This allows the Gray value estimation model to be updated at an appropriate timing by using the variability of the estimated values ​​as the reference value.

[0069] The gray value estimation model creation unit 111 may determine that the gray value estimation model should be updated if the summarized amount of the estimation error Δx of multiple background images newly acquired by the background image acquisition unit 101 is more than a predetermined multiple compared to a reference value. This allows the gray value estimation model to be updated at an appropriate timing using the variability of the estimated values ​​as a reference value.

[0070] The grayscale value estimation model creation unit 111 may further create a difference prediction model that predicts the estimation error Δx and estimation error Δy when the summation amount of the estimation error Δx of multiple background images newly acquired by the background image acquisition unit 101 is more than a predetermined value greater than the reference value. The grayscale value estimation model creation unit 111 may update the color change estimation model using the difference prediction model. With this configuration, the grayscale value estimation model can be appropriately updated without using all data as training material.

[0071] The grayscale value estimation model creation unit 111 may further create a difference prediction model that predicts the estimation error Δy based on the estimation error Δx when the summation amount of the estimation error Δx of multiple background images newly acquired by the background image acquisition unit 101 is greater than or equal to a predetermined value compared to a reference value. The grayscale value estimation model creation unit 111 may update the color change estimation model using the difference prediction model. With this configuration, the grayscale value estimation model can be appropriately updated without using all data as training material.

[0072] The Gray value estimation model creation unit 111 may exclude workpieces W in which at least one of the estimation error Δx and estimation error Δy is greater than a predetermined value from the multiple workpieces W used for training. This makes it possible to create a Gray value estimation model while excluding outliers.

[0073] The gray value estimation model creation unit 111 may calculate the estimation error Δxnew, which is the difference between the measured value and the estimated value in the background image, based on the updated gray value estimation model, and may also calculate the estimation error Δynew, which is the difference between the measured value and the estimated value in the processed image. If there is a workpiece W where at least one of the estimation error Δxnew and the estimation error Δynew is greater than a predetermined value, the gray value estimation model creation unit 111 may discard the updated gray value estimation model and create a gray value estimation model again. With this configuration, it is possible to discard the gray value estimation model created considering outliers and create a suitable gray value estimation model again while removing the outliers.

[0074] The Gray value estimation model creation unit 111 may create a Gray value estimation model for each shot or for each workpiece W. This allows for the creation of an appropriate Gray value estimation model according to the operating environment and other factors.

[0075] The CD estimation model creation unit 112 may create a CD estimation model for each shot or for each workpiece W. This allows for the creation of an appropriate CD estimation model according to the usage environment and other factors.

[0076] The coating and developing apparatus 2 may be configured to include one or more devices, at least a post-processing image acquisition unit 102 and a background image acquisition unit 101, and a server provided separately from the apparatus, which holds at least a gray value estimation model and a CD estimation model. This allows for the selection of an appropriate apparatus configuration depending on the operating environment.

[0077] Finally, various exemplary embodiments included in this disclosure are described below in [E1] to [E13].

[0078] [E1] An estimation model creation apparatus for a shape characteristic value estimation model that estimates shape characteristic values, which are characteristic values ​​relating to the shape of a target film that has been film-treated on a substrate, comprising: a post-processing image acquisition unit that acquires a post-processing image, which is image information relating to the surface of a film-treated substrate; a pre-processing image acquisition unit that acquires a pre-processing image, which is image information relating to the surface of a substrate before film treatment; a color change estimation model creation unit that creates a color change estimation model that estimates information relating to the surface color of a substrate included in the post-processing image from information relating to the surface color of a substrate included in the pre-processing image by learning information relating to the surface color of the substrate included in the pre-processing image and information relating to the surface color of the substrate included in the post-processing image for each of the plurality of substrates for learning; a reference value calculation unit that calculates a reference value for updating the color change estimation model based on the pre-processing images of the plurality of substrates for learning; and a correlation estimation model creation unit that calculates the difference between the measured value of the information relating to the surface color of the substrate included in the post-processing image and the result estimated by the color change estimation model, and creates a correlation estimation model that estimates the correlation between the difference and the shape characteristic value of the target film that has been film-treated, The color change estimation model creation unit determines whether or not to update the color change estimation model based on the pre-processing image newly acquired by the pre-processing image acquisition unit and the reference value calculated by the reference value calculation unit, and if it determines that it should be updated, it updates the color change estimation model using the newly acquired pre-processing image.

[0079] [E2] The color change estimation model creation unit creates a color change estimation model that further estimates information relating to the surface color of the substrate included in the pre-processing image, and for each of the plurality of substrates for learning, calculates an estimation error Δx, which is the difference between the measured value and the estimated value in the pre-processing image, and an estimation error Δy, which is the difference between the measured value and the estimated value in the post-processing image, based on the color change estimation model, as described in [E1].

[0080] [E3] The estimation model creation apparatus according to [E2], wherein the reference value calculation unit calculates a summary amount of the estimation error Δx for each of the plurality of learning boards, and sets the summary amount as the reference value.

[0081] [E4] The color change estimation model creation device according to [E3], wherein the color change estimation model creation unit determines that the color change estimation model should be updated when the summation amount of the estimation error Δx of a plurality of pre-processed images newly acquired by the pre-processed image acquisition unit is greater than or equal to a predetermined value compared with the reference value.

[0082] [E5] The color change estimation model creation device according to [E4], wherein the color change estimation model creation unit further creates a difference prediction model that predicts the estimation error Δx and estimation error Δy when the summation amount of the estimation error Δx of a plurality of pre-processed images newly acquired by the pre-processed image acquisition unit is greater than or equal to a predetermined value compared with the reference value, and updates the color change estimation model using the difference prediction model.

[0083] [E6] The color change estimation model creation device according to [E4], wherein the color change estimation model creation unit further creates a difference prediction model that predicts the estimation error Δy based on the estimation error Δx when the summation amount of the estimation error Δx of a plurality of pre-processed images newly acquired by the pre-processed image acquisition unit is greater than or equal to a predetermined value compared with the reference value, and updates the color change estimation model using the difference prediction model.

[0084] [E7] The estimation model creation apparatus according to any one of [E2] to [E6], wherein the color change estimation model creation unit excludes from the plurality of learning substrates any substrate in which at least one of the estimation error Δx and the estimation error Δy is greater than a predetermined value.

[0085] [E8] The color change estimation model creation unit calculates an estimation error Δxnew, which is the difference between the measured value and the estimated value in the pre-processed image, and an estimation error Δynew, which is the difference between the measured value and the estimated value in the post-processed image, based on the updated color change estimation model, and if there is a substrate in which at least one of the estimation error Δxnew and the estimation error Δynew is greater than a predetermined value, the updated color change estimation model is discarded and the color change estimation model is created again, as described in [E5] or [E6].

[0086] [E9] The color change estimation model creation unit creates the color change estimation model for each shot or for each substrate, as described in any one of [E1] to [E8].

[0087] [E10] The correlation estimation model creation unit creates the correlation estimation model for each shot or for each substrate, as described in any one of [E1] to [E9].

[0088] [E11] An estimation model creation apparatus according to any one of [E1] to [E10], comprising one or more devices including at least the post-processing image acquisition unit and the pre-processing image acquisition unit, and a server provided separately from the one or more devices, which holds at least the color change estimation model and the correlation estimation model.

[0089] [E12] A method for creating an estimation model relating to a shape characteristic value estimation model for estimating a shape characteristic value which is a characteristic value relating to the shape of a target film that has been film-treated on a substrate, comprising: acquiring a post-processing image which is image information relating to the surface of a film-treated substrate; acquiring a pre-processing image which is image information relating to the surface of a substrate before film treatment; creating a color change estimation model that estimates information relating to the surface color of a substrate contained in the post-processing image from information relating to the surface color of a substrate contained in the pre-processing image by learning information relating to the surface color of the substrate contained in the pre-processing image and information relating to the surface color of the substrate contained in the post-processing image for each of the multiple substrates for learning; calculating a reference value for updating the color change estimation model based on the pre-processing images of the multiple substrates for learning; and creating a correlation estimation model that calculates the difference between the measured value of the information relating to the surface color of the substrate contained in the post-processing image and the result estimated by the color change estimation model, and estimates the correlation between the difference and the shape characteristic value of the film-treated target film, A method for creating an estimation model, comprising determining whether or not to update the color change estimation model based on the newly acquired pre-processed image and the calculated reference value, and updating the color change estimation model using the newly acquired pre-processed image if it is determined that it should be updated.

[0090] [E13] A computer-readable storage medium containing a program for causing the device to execute the estimation model creation method described in [E12].

[0091] 2...Coating and developing device (estimated model creation device), 101...Underlay image acquisition unit (pre-processing image acquisition unit), 102...Post-processing image acquisition unit, 107...Reference value calculation unit, 111...Gray value estimation model creation unit (color change estimation model creation unit), 112...CD estimation model creation unit (correlation estimation model creation unit).

Claims

1. An estimation model creation apparatus for a shape characteristic value estimation model that estimates shape characteristic values, which are characteristic values ​​relating to the shape of a target film that has been film-treated on a substrate, comprising: a post-processing image acquisition unit that acquires a post-processing image, which is image information relating to the surface of a film-treated substrate; a pre-processing image acquisition unit that acquires a pre-processing image, which is image information relating to the surface of a substrate before film treatment; a color change estimation model creation unit that creates a color change estimation model that estimates information relating to the surface color of a substrate contained in the post-processing image from information relating to the surface color of a substrate contained in the pre-processing image, by learning information relating to the surface color of the substrate contained in the pre-processing image and information relating to the surface color of the substrate contained in the post-processing image for each of the multiple substrates for learning; a reference value calculation unit that calculates a reference value for updating the color change estimation model based on the pre-processing images of the multiple substrates for learning; and a correlation estimation model creation unit that calculates the difference between the measured value of the information relating to the surface color of the substrate contained in the post-processing image and the result estimated by the color change estimation model, and creates a correlation estimation model that estimates the correlation between the difference and the shape characteristic value of the target film that has been film-treated, The color change estimation model creation unit determines whether or not to update the color change estimation model based on the pre-processing image newly acquired by the pre-processing image acquisition unit and the reference value calculated by the reference value calculation unit, and if it determines that it should be updated, it updates the color change estimation model using the newly acquired pre-processing image.

2. The color change estimation model creation unit creates a color change estimation model that further estimates information relating to the surface color of the substrate included in the pre-processing image, and for each of the plurality of substrates for learning, calculates an estimation error Δx, which is the difference between the measured value and the estimated value in the pre-processing image, and calculates an estimation error Δy, which is the difference between the measured value and the estimated value in the post-processing image, based on the color change estimation model, the estimation model creation device according to claim 1.

3. The estimation model creation apparatus according to claim 2, wherein the reference value calculation unit calculates a summary amount of the estimation error Δx for each of the plurality of learning boards, and sets the summary amount as the reference value.

4. The color change estimation model creation device according to claim 3, wherein the color change estimation model creation unit determines that the color change estimation model should be updated when the summation amount of the estimation error Δx of a plurality of pre-processed images newly acquired by the pre-processed image acquisition unit is greater than or equal to a predetermined value compared with the reference value.

5. The estimation model creation device according to claim 4, wherein the color change estimation model creation unit further creates a difference prediction model that predicts the estimation error Δx and estimation error Δy when the summation amount of the estimation error Δx of a plurality of pre-processed images newly acquired by the pre-processed image acquisition unit is greater than or equal to a predetermined value compared with the reference value, and updates the color change estimation model using the difference prediction model.

6. The estimation model creation device according to claim 4, wherein the color change estimation model creation unit further creates a difference prediction model that predicts the estimation error Δy based on the estimation error Δx when the summation amount of the estimation error Δx of a plurality of pre-processed images newly acquired by the pre-processed image acquisition unit is greater than or equal to a predetermined value compared with the reference value, and updates the color change estimation model using the difference prediction model.

7. The estimation model creation apparatus according to claim 2, wherein the color change estimation model creation unit excludes from the plurality of learning substrates any substrate in which at least one of the estimation error Δx and the estimation error Δy is greater than a predetermined value.

8. The color change estimation model creation device according to claim 5 or 6, wherein the color change estimation model creation unit calculates an estimation error Δxnew, which is the difference between the measured value and the estimated value in the pre-processed image, and calculates an estimation error Δynew, which is the difference between the measured value and the estimated value in the post-processed image, based on the updated color change estimation model, and if there is a substrate in which at least one of the estimation error Δxnew and the estimation error Δynew is greater than a predetermined value, the updated color change estimation model is discarded and the color change estimation model is created again.

9. The estimation model creation apparatus according to claim 1, wherein the color change estimation model creation unit creates the color change estimation model for each shot or for each substrate.

10. The estimation model creation apparatus according to claim 1, wherein the correlation estimation model creation unit creates the correlation estimation model for each shot or for each substrate.

11. An estimation model creation apparatus according to claim 1, comprising one or more devices including at least the post-processing image acquisition unit and the pre-processing image acquisition unit, and a server provided separately from the one or more devices, which holds at least the color change estimation model and the correlation estimation model.

12. A method for creating an estimation model relating to a shape characteristic value estimation model for estimating a shape characteristic value which is a characteristic value relating to the shape of a target film that has been film-treated on a substrate, comprising: acquiring a post-processing image which is image information relating to the surface of a film-treated substrate; acquiring a pre-processing image which is image information relating to the surface of a substrate before film treatment; creating a color change estimation model that estimates the information relating to the surface of the substrate contained in the post-processing image from the information relating to the surface of the substrate contained in the pre-processing image by learning the information relating to the surface color of the substrate contained in the pre-processing image and the information relating to the surface color of the substrate contained in the post-processing image for each of the multiple substrates for training; calculating a reference value for updating the color change estimation model based on the pre-processing images of the multiple substrates for training; and creating a correlation estimation model that calculates the difference between the measured value of the information relating to the surface color of the substrate contained in the post-processing image and the result estimated by the color change estimation model, and estimates the correlation between the difference and the shape characteristic value of the target film that has been film-treated, A method for creating an estimation model, comprising determining whether or not to update the color change estimation model based on the newly acquired pre-processed image and the calculated reference value, and updating the color change estimation model using the newly acquired pre-processed image if it is determined that it should be updated.

13. A computer-readable storage medium storing a program for causing a device to execute the estimation model creation method described in claim 12.

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