Ferroelectric film thickness identification method based on multi-index comprehensive scoring equation

Abstract

The invention discloses a ferroelectric film thickness identification method based on a multi-index comprehensive scoring equation, and belongs to the technical field of ferroelectric material characterization and machine learning. The method comprises the steps that an optical imaging device collects an optical image of the surface of the ferroelectric film, data preprocessing, data enhancement processing and manual labeling processing are carried out on the image, and a data set system is constructed; establishing a multi-index comprehensive scoring equation including a root-mean-square error (RMSE), a mean absolute error (MAE), a decision coefficient (R2) and a mean absolute percentage error (MAPE), and performing global optimization on training parameters of the machine learning regression model in combination with grid search; and performing thickness value prediction on the to-be-predicted image by using the obtained optimization model. The ferroelectric film thickness identification method has the characteristics of simplicity, convenience, reliability, no contact, no damage and low deviation, and has a wide application prospect in the technical field of ferroelectric material characterization.

Description

Technical Field

[0001] The present invention relates to the field of ferroelectric material characterization and machine learning technology, and more particularly to a ferroelectric film thickness identification method based on a multi-index comprehensive scoring equation. Background Art

[0002] Ferroelectric thin films, due to their unique ferroelectric, dielectric, and piezoelectric properties, have important applications in nonvolatile memory, capacitors, and sensors. The ferroelectric properties of ferroelectric thin films are influenced by many factors, with film thickness becoming an increasingly important parameter influencing their performance. Therefore, establishing a reliable thickness characterization system provides a crucial methodological foundation for accurately quantifying the structural parameters of ferroelectric thin films.

[0003] At present, the main methods for characterizing the thickness of ferroelectric films include atomic force microscopy, scanning electron microscopy, ellipsometers, and optical profilometers. Atomic force microscopy and scanning electron microscopy characterization methods can provide thickness information with nanometer-level resolution, but they require the preparation of cross-sectional samples and the detection process is complicated. Although ellipsometer and optical profilometer characterization methods have the advantage of non-contact measurement, their point / line scanning modes make it difficult to achieve full coverage of the substrate and require repeated calibration and model fitting. Existing ferroelectric film thickness characterization technologies have difficulty in balancing measurement efficiency, non-destructiveness, and high-throughput detection. In summary, this field urgently needs a non-contact ferroelectric film thickness identification method that can be both simple to operate and maintain the integrity of the film. Summary of the Invention

[0004] In view of the above problems, the purpose of the present invention is to provide a ferroelectric thin film thickness identification method based on a multi-index comprehensive scoring equation to solve the shortcomings of the existing technology in the above background technology.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A ferroelectric film thickness identification method based on a multi-index comprehensive scoring equation comprises:

[0007] Optical imaging equipment collects optical images of the ferroelectric thin film surface;

[0008] Perform data preprocessing, data enhancement, and manual annotation on images to build a dataset system;

[0009] Establish a system including root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R 2 ) and the mean absolute percentage error (MAPE) of the multi-index comprehensive scoring equation;

[0010] Combined with grid search to globally optimize the training parameters of machine learning regression models;

[0011] The obtained optimized model is used to predict the thickness of the image to be predicted.

[0012] Furthermore, the multi-index comprehensive scoring equation specifically includes:

[0013] The formula of the multi-index comprehensive scoring equation is as follows:

[0014] A=x×RMSE+y×MAE+z×R 2 +w×MAPE

[0015] Among them, A is a comprehensive score obtained by weighted summation of the four indicators; RMSE represents the root mean square error between the measured value and the predicted value on the validation set; MAE represents the mean absolute error between the measured value and the predicted value on the validation set; R 2 Represents the coefficient of determination on the validation set; MAPE represents the mean absolute percentage error between the measured and predicted values on the validation set;

[0016] In the multi-index comprehensive scoring equation, RMSE accounts for weight x, MAE accounts for weight y, R 2 Occupies weight z, MAPE occupies weight w;

[0017] The range of the variable z is 0.2≤z≤0.7, and the total weight x+y+z+w=1.

[0018] Furthermore, the ferroelectric thin film is any one of BaTiO3, BiFeO3, PbTiO3, Pb(Zr,Ti)O3, (Hf,Zr)O2, and has a thickness of 1-450 nm.

[0019] Furthermore, the optical imaging device collects an optical image of the surface of the ferroelectric thin film, specifically comprising:

[0020] An optical microscope and a high-resolution camera are used to collect optical images of the surface of the ferroelectric thin film. The resolution of the obtained optical image is not less than 3840×2160 pixels, and the physical size of a single pixel is 2μm×2μm.

[0021] According to the thickness information of the ferroelectric thin film, the collected optical images are classified to obtain a ferroelectric thin film optical image dataset.

[0022] Furthermore, the data preprocessing specifically includes:

[0023] Data cleaning: remove duplicate and invalid images;

[0024] Image normalization: The cleaned image resolution is uniformly converted to 512 × 512 pixels and normalized;

[0025] Dataset division: The ferroelectric thin film optical image dataset obtained after the above processing is divided into a training optical image dataset, a verification optical image dataset, and a test optical image dataset.

[0026] Furthermore, the data enhancement processing specifically includes:

[0027] Perform random rotation (angle range 0°≤θ≤180°), flip (horizontally / vertically), scaling and cropping (scaling ratio 0.8-1.2), and brightness perturbation (ΔL±15%) operations on the images in the training optical image dataset and the validation optical image dataset;

[0028] The image size is then adjusted twice to ensure that the output image size is 224×224 pixels, and finally the training optical image enhancement dataset and the verification optical image enhancement dataset are obtained.

[0029] Furthermore, the manual annotation process specifically includes:

[0030] According to the thickness information of the images in the training optical image enhancement dataset, the verification optical image enhancement dataset and the test optical image dataset, the images are manually annotated to obtain the dataset system, which includes a training set, a verification set and a test set.

[0031] Furthermore, the machine learning regression model specifically includes:

[0032] The machine learning regression model is a convolutional neural network regression model;

[0033] The convolutional neural network regression model adopts a three-level convolutional feature extraction architecture: the first feature extraction layer contains a 32-channel 3×3 convolution kernel and a 2×2 pooling layer; the second feature extraction layer is configured with a 64-channel 3×3 convolution kernel and a 2×2 pooling layer; the third feature extraction layer deploys a 128-channel 3×3 convolution kernel; the feature tensor is topologically converted from three-dimensional spatial features to one-dimensional vectors through the Flatten layer, and finally the feature space mapping is completed through a fully connected layer with 128 hidden units.

[0034] Furthermore, the grid search is combined to globally optimize the training parameters of the machine learning regression model, specifically including:

[0035] traversing preset parameter combinations through grid search, performing model training iterations on the training set, and quantitatively evaluating film thickness prediction performance based on the validation set;

[0036] Analyze the performance evaluation indicators of the model under each set of parameter combinations, and combine the comprehensive score value to obtain the optimal parameter combination of the machine learning regression model.

[0037] Furthermore, the method of using the obtained optimization model to predict the thickness value of the image to be predicted specifically includes:

[0038] Based on the optimal parameter combination, model training is performed according to the training set and the validation set to obtain an optimized model;

[0039] The optical image of the film to be predicted in the test set is input into the optimization model to obtain the corresponding thickness prediction value.

[0040] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation, which specifically includes the following beneficial effects:

[0041] 1. The present invention realizes non-destructive characterization of the thickness of ferroelectric films, overcomes the limitations of traditional destructive characterization methods, and shows significant application potential in the field of ferroelectric material characterization technology.

[0042] 2. The present invention can realize the thickness characterization of the ferroelectric film by relying only on the optical image data of the ferroelectric film surface, effectively reducing the operational professional requirements for the thickness characterization of the ferroelectric film and simultaneously reducing the time cost and economic cost.

[0043] 3. The present invention constructs a multi-index comprehensive scoring equation to avoid the local optimal trap of regression model training and effectively improve the film thickness recognition accuracy and result reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0045] Figure 1 A schematic diagram of the regression model training process provided by an embodiment of the present invention;

[0046] Figure 2 The back propagation (BP) neural network model obtained in Example 1 provided in the embodiment of the present invention is a scatter plot of the thickness measured values and the thickness predicted values in the test set data and the recognition results of four groups of typical samples are visualized;

[0047] Figure 3 The support vector regression (SVR) model obtained in Example 2 provided in the embodiment of the present invention is a scatter plot of the thickness measured values and the thickness predicted values in the test set data and the recognition results of four groups of typical samples are visualized;

[0048] Figure 4The convolutional neural network (CNN) model obtained in Example 3 provided in the embodiment of the present invention is visualized by a scatter plot of the measured thickness values and the predicted thickness values in the test set data and the recognition results of 4 groups of typical samples. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0050] Example 1

[0051] Embodiment 1 of the present invention discloses a method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation, specifically comprising:

[0052] S1. Optical imaging equipment collects optical images of the ferroelectric thin film surface, performs data preprocessing, data enhancement processing, and manual annotation processing on the images to build a data set system;

[0053] S2, establish a system including root mean square error (RMSE), mean absolute error (MAE), determination coefficient (R 2 ) and mean absolute percentage error (MAPE) multi-index comprehensive scoring equation, combined with grid search to globally optimize the training parameters of the machine learning regression model;

[0054] S3. Use the obtained optimization model to predict the thickness value of the image to be predicted.

[0055] Next, each training step of the above regression model is explained respectively.

[0056] In the above step S1, the following contents are specifically included:

[0057] (1) Optical imaging equipment collects optical images of the ferroelectric thin film surface, specifically including:

[0058] The ferroelectric thin film is selected as BaTiO3 with a thickness of 1-450nm;

[0059] An optical microscope and a high-resolution camera were used to collect optical images of the ferroelectric thin film surface. The obtained optical image resolution was 3840 × 2160 pixels, and the physical size of a single pixel was 2 μm × 2 μm.

[0060] According to the thickness information of the ferroelectric film, the collected optical images are classified to obtain a ferroelectric film optical image dataset;

[0061] (2) Perform data preprocessing, including:

[0062] Data cleaning: remove duplicate and invalid images;

[0063] Image normalization: The cleaned image resolution is uniformly converted to 512 × 512 pixels and normalized;

[0064] Dataset division: Using a stratified sampling method, the ferroelectric thin film optical image dataset obtained after the above processing is divided into a training optical image dataset, a verification optical image dataset, and a test optical image dataset. For example, 80% of the ferroelectric thin film optical image data is randomly divided into a training optical image dataset, 10% of the data is randomly divided into a verification optical image dataset, and 10% of the data is randomly divided into a test optical image dataset, to ensure the randomness and class balance of the data in the training optical image dataset, the verification optical image dataset, and the test optical image dataset.

[0065] (3) Perform data enhancement processing, including:

[0066] Perform random rotation (angle range 0°≤θ≤180°), flip (horizontally / vertically), scaling and cropping (scaling ratio 0.8-1.2), and brightness perturbation (ΔL±15%) operations on the images in the training optical image dataset and the validation optical image dataset;

[0067] The image size is then resized to ensure that the output image size is 224×224 pixels, and finally the training optical image enhancement dataset and the verification optical image enhancement dataset are obtained;

[0068] (4) Perform manual annotation processing, including:

[0069] According to the thickness information of the images in the training optical image enhancement dataset, the verification optical image enhancement dataset and the test optical image dataset, the images are manually annotated to obtain the dataset system, which includes a training set, a verification set and a test set.

[0070] In the above step S2, the following contents are specifically included:

[0071] (1) Select a machine learning regression model, such as a back propagation (BP) neural network regression model;

[0072] The BP regression model training parameters are specifically set as follows: Learning_rate (learning rate) = 1e-3, Batch_size (batch size) = 8, Epoch (iteration number) = 100, λ (L2 regularization coefficient) = 1e-2;

[0073] (2) Establish a model including RMSE, MAE, R2 And MAPE's multi-index comprehensive scoring equation, specifically including:

[0074] The formula of the multi-index comprehensive scoring equation is as follows:

[0075] A BP =0.3×RMSE+0.3×MAE+0.2×R 2 +0.2×MAPE

[0076] Among them, A BP It is a comprehensive score obtained by weighted summation of the four indicators; RMSE represents the root mean square error between the measured value and the predicted value on the validation set; MAE represents the mean absolute error between the measured value and the predicted value on the validation set; R 2 Represents the coefficient of determination on the validation set; MAPE represents the mean absolute percentage error between the measured and predicted values on the validation set;

[0077] In the multi-index comprehensive scoring equation, RMSE accounts for 30% of the weight, MAE accounts for 30% of the weight, R 2 The weight is 20%, and the MAPE weight is 20%;

[0078] The multi-index comprehensive scoring equation scores the training results of the current parameter combination, where the total weight of RMSE, MAE and MAPE accounts for 80%, R 2 The weight of is 20%, and the smaller the score, the better the performance of the model;

[0079] (3) Based on the comprehensive score value obtained by the multi-index comprehensive scoring equation, the training parameters of the machine learning regression model are globally optimized in combination with grid search to obtain the optimal parameter combination of the model, including:

[0080] traversing preset parameter combinations through grid search, performing model training iterations on the training set, and quantitatively evaluating film thickness prediction performance based on the validation set;

[0081] Analyze the performance evaluation indicators of the model under each set of parameter combinations, and combine the comprehensive score to obtain the optimal parameter combination of the machine learning regression model;

[0082] Finally, the model score value A under each set of parameter combinations BP As a guide for optimal parameter selection, the optimal parameter combination of the BP regression model is obtained: Learning_rate (learning rate) = 1e-3, Batch_size (batch size) = 4, Epoch (number of iterations) = 300, λ (L2 regularization coefficient) = 1e-3.

[0083] In the above step S3, the following contents are specifically included:

[0084] Based on the optimal parameter combination obtained above, model training is performed according to the training set and the validation set to obtain the optimal BP model as the optimization model; the optical image of the film to be predicted in the test set is input into the optimization model to obtain the corresponding thickness prediction value;

[0085] (1) Model training, specifically including: setting the training parameters of the BP regression model to the optimal parameter combination in step S2, i.e., Learning_rate (learning rate) = 1e-3, Batch_size (batch size) = 4, Epoch (number of iterations) = 300, λ (L2 regularization coefficient) = 1e-3, and then training the model based on the training set and the validation set to obtain the optimal BP model as the optimization model;

[0086] (2) Model prediction, specifically including: inputting the optical image of the film to be predicted in the test set into the optimization model to obtain the corresponding film thickness prediction value.

[0087] like Figure 2 The figure shows the scatter plot of the thickness measured value and the thickness predicted value of the BP model in the test set data in Example 1 and the visualization of the recognition results of 4 groups of typical samples. The MSE of the BP model in the test set data is 0.0065, MAE is 0.0488, RMSE is 0.0809, MBE is -0.0435, R 2 =0.9087; Figure 2 Figure (a) shows the scatter plot of the measured thickness values and the predicted thickness values of the BP model in the test set data; Figure 2 Figure (b) shows the visualization of the identification results of four typical groups of samples. The measured thickness values are 78nm, 231nm, 239nm and 276nm, and the corresponding predicted thickness values are 74.80nm, 232.77nm, 235.40nm and 279.88nm, respectively. The low coefficient of determination and high error value indicate that the BP model has poor accuracy in identifying the thickness of BaTiO3 films.

[0088] Example 2

[0089] Embodiment 2 of the present invention discloses a method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation, specifically comprising:

[0090] S1. Optical imaging equipment collects optical images of the ferroelectric thin film surface, performs data preprocessing, data enhancement processing, and manual annotation processing on the images to build a data set system;

[0091] S2, establish a system including root mean square error (RMSE), mean absolute error (MAE), determination coefficient (R 2) and mean absolute percentage error (MAPE) multi-index comprehensive scoring equation, combined with grid search to globally optimize the training parameters of the machine learning regression model;

[0092] S3. Use the obtained optimization model to predict the thickness value of the image to be predicted.

[0093] Next, each training step of the above regression model is explained respectively.

[0094] In the above step S1, the following contents are specifically included:

[0095] (1) Optical imaging equipment collects optical images of the ferroelectric thin film surface, specifically including:

[0096] The ferroelectric thin film is selected as BaTiO3 with a thickness of 1-450nm;

[0097] An optical microscope and a high-resolution camera were used to collect optical images of the ferroelectric thin film surface. The obtained optical image resolution was 3840 × 2160 pixels, and the physical size of a single pixel was 2 μm × 2 μm.

[0098] According to the thickness information of the ferroelectric film, the collected optical images are classified to obtain a ferroelectric film optical image dataset;

[0099] (2) Perform data preprocessing, including:

[0100] Data cleaning: remove duplicate and invalid images;

[0101] Image normalization: The cleaned image resolution is uniformly converted to 512 × 512 pixels and normalized;

[0102] Dataset Division: Using a stratified sampling method, the ferroelectric thin film optical image dataset obtained after the above processing is divided into a training optical image dataset, a validation optical image dataset, and a test optical image dataset. For example, 80% of the ferroelectric thin film optical image dataset is randomly divided into a training optical image dataset, 10% of the data is randomly divided into a validation optical image dataset, and 10% of the data is randomly divided into a test optical image dataset, ensuring randomness and class balance among the training optical image dataset, validation optical image dataset, and test optical image dataset.

[0103] (3) Perform data enhancement processing, including:

[0104] Perform random rotation (angle range 0°≤θ≤180°), flip (horizontally / vertically), scaling and cropping (scaling ratio 0.8-1.2), and brightness perturbation (ΔL±15%) operations on the images in the training optical image dataset and the validation optical image dataset;

[0105] The image size is then resized to ensure that the output image size is 224×224 pixels, and finally the training optical image enhancement dataset and the verification optical image enhancement dataset are obtained;

[0106] (4) Perform manual annotation processing, including:

[0107] According to the thickness information of the images in the training optical image enhancement dataset, the verification optical image enhancement dataset and the test optical image dataset, the images are manually annotated to obtain the dataset system, which includes a training set, a verification set and a test set.

[0108] In the above step S2, the following contents are specifically included:

[0109] (1) Select a machine learning regression model, such as a support vector regression (SVR) regression model;

[0110] The SVR regression model training parameters are specifically set as follows: Kernel (kernel function type) = 'Linear', C (penalty coefficient) = 0.1, Epsilon (ε-insensitive loss function) = 0.05, Gamma (kernel function coefficient) = 'Scale';

[0111] (2) Establish a model including RMSE, MAE, R 2 And MAPE's multi-index comprehensive scoring equation, specifically including:

[0112] The formula of the multi-index comprehensive scoring equation is as follows:

[0113] A SVR =0×RMSE+0.3×MAE+0.7×R 2 +0×MAPE

[0114] Among them, A SVR It is a comprehensive score obtained by weighted summation of the four indicators; RMSE represents the root mean square error between the measured value and the predicted value on the validation set; MAE represents the mean absolute error between the measured value and the predicted value on the validation set; R 2 Represents the coefficient of determination on the validation set; MAPE represents the mean absolute percentage error between the measured and predicted values on the validation set;

[0115] In the multi-index comprehensive scoring equation, RMSE accounts for 0 weight, MAE accounts for 30% weight, R 2 The weight is 70%, and the MAPE weight is 0;

[0116] The scoring equation scores the training results of the current parameter combination, where R 2The weight of is 70%, and the larger the score, the better the performance of the model;

[0117] (3) Based on the comprehensive score value obtained by the multi-index comprehensive scoring equation, the training parameters of the machine learning regression model are globally optimized in combination with grid search to obtain the optimal parameter combination of the model, including:

[0118] traversing preset parameter combinations through grid search, performing model training iterations on the training set, and quantitatively evaluating film thickness prediction performance based on the validation set;

[0119] Analyze the performance evaluation indicators of the model under each set of parameter combinations, and combine the comprehensive score to obtain the optimal parameter combination of the machine learning regression model;

[0120] Finally, the model score value A under each set of parameter combinations SVR As a guide for optimal parameter selection, the optimal parameter combination of the SVR regression model was obtained: Kernel (kernel function type) = 'RBF', C (penalty coefficient) = 10, Epsilon (ε-insensitive loss function) = 0.01, Gamma (kernel function coefficient) = 0.1.

[0121] In the above step S3, the following contents are specifically included:

[0122] Based on the optimal parameter combination obtained above, model training is performed according to the training set and the validation set to obtain the optimal SVR model as the optimization model; the optical image of the film to be predicted in the test set is input into the optimization model to obtain the corresponding thickness prediction value;

[0123] (1) Model training, specifically including: setting the training parameters of the SVR regression model to the optimal parameter combination in step S2, namely, Kernel (kernel function type) = 'RBF', C (penalty coefficient) = 10, Epsilon (ε-insensitive loss function) = 0.01, Gamma (kernel function coefficient) = 0.1, and then training the model based on the training set and the validation set to obtain the optimal SVR model as the optimization model;

[0124] (2) Model prediction, specifically including: inputting the optical image of the film to be predicted in the test set into the optimization model to obtain the corresponding film thickness prediction value.

[0125] like Figure 3 The figure shows the scatter plot of the thickness measured value and the thickness predicted value of the SVR model in the test set data in Example 2 and the visualization of the recognition results of four groups of typical samples. The SVR model has MSE=0.0032, MAE=0.0294, RMSE=0.0566, R 2 =0.9614; Figure 3Figure (a) shows the scatter plot of the measured thickness values and the predicted thickness values of the SVR model in the test set data; Figure 3 Figure (b) shows the visualization of the identification results of four typical groups of samples. The measured thickness values are 62nm, 153nm, 264nm and 309nm, and the corresponding predicted thickness values are 61.63nm, 153.58nm, 262.92nm and 309.95nm. The coefficient of determination close to 1 and the low error value indicate the high accuracy of the SVR model in identifying the thickness of BaTiO3 films.

[0126] Example 3

[0127] Embodiment 3 of the present invention discloses a method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation, which specifically includes:

[0128] S1. Optical imaging equipment collects optical images of the ferroelectric thin film surface, performs data preprocessing, data enhancement processing, and manual annotation processing on the images to build a data set system;

[0129] S2, establish a system including root mean square error (RMSE), mean absolute error (MAE), determination coefficient (R 2 ) and mean absolute percentage error (MAPE) multi-index comprehensive scoring equation, combined with grid search to globally optimize the training parameters of the machine learning regression model;

[0130] S3. Use the obtained optimization model to predict the thickness value of the image to be predicted.

[0131] Next, each training step of the above regression model is explained respectively.

[0132] In the above step S1, the following contents are specifically included:

[0133] (1) Optical imaging equipment collects optical images of the ferroelectric thin film surface, specifically including:

[0134] The ferroelectric thin film is selected as BaTiO3 with a thickness of 1-450nm;

[0135] An optical microscope and a high-resolution camera were used to collect optical images of the ferroelectric thin film surface. The obtained optical image resolution was 3840 × 2160 pixels, and the physical size of a single pixel was 2 μm × 2 μm.

[0136] According to the thickness information of the ferroelectric film, the collected optical images are classified to obtain a ferroelectric film optical image dataset;

[0137] (2) Perform data preprocessing, including:

[0138] Data cleaning: remove duplicate and invalid images;

[0139] Image normalization: The cleaned image resolution is uniformly converted to 512 × 512 pixels and normalized;

[0140] Dataset Division: Using a stratified sampling method, the ferroelectric thin film optical image dataset obtained after the above processing is divided into a training optical image dataset, a validation optical image dataset, and a test optical image dataset. For example, 80% of the ferroelectric thin film optical image dataset is randomly divided into a training optical image dataset, 10% of the data is randomly divided into a validation optical image dataset, and 10% of the data is randomly divided into a test optical image dataset, ensuring randomness and class balance among the training optical image dataset, validation optical image dataset, and test optical image dataset.

[0141] (3) Perform data enhancement processing, including:

[0142] Perform random rotation (angle range 0°≤θ≤180°), flip (horizontally / vertically), scaling and cropping (scaling ratio 0.8-1.2), and brightness perturbation (ΔL±15%) operations on the images in the training optical image dataset and the validation optical image dataset;

[0143] The image size is then resized to ensure that the output image size is 224×224 pixels, and finally the training optical image enhancement dataset and the verification optical image enhancement dataset are obtained;

[0144] (4) Perform manual annotation processing, including:

[0145] According to the thickness information of the images in the training optical image enhancement dataset, the verification optical image enhancement dataset and the test optical image dataset, the images are manually annotated to obtain the dataset system, which includes a training set, a verification set and a test set.

[0146] In the above step S2, the following contents are specifically included:

[0147] (1) Select a machine learning regression model, such as a convolutional neural network (CNN) regression model;

[0148] The CNN regression model uses a three-level convolutional feature extraction architecture: the first feature extraction layer contains a 32-channel 3×3 convolution kernel and a 2×2 pooling layer; the second feature extraction layer is configured with a 64-channel 3×3 convolution kernel and a 2×2 pooling layer; the third feature extraction layer deploys a 128-channel 3×3 convolution kernel. The feature tensor is topologically converted from three-dimensional spatial features to one-dimensional vectors through a Flatten layer, and finally the feature space mapping is completed through a fully connected layer with 128 hidden units.

[0149] The specific training parameters of the CNN regression model are set as follows: Learning_rate = 1e-3, Batch_size = 32, Epoch = 50, Optimizer = 'Adam';

[0150] (2) Establish a model including RMSE, MAE, R 2 And MAPE's multi-index comprehensive scoring equation, specifically including:

[0151] The formula of the multi-index comprehensive scoring equation is as follows:

[0152] A CNN =0.3×RMSE+0.3×MAE+0.2×R 2 +0.2×MAPE

[0153] Among them, A CNN It is a comprehensive score obtained by weighted summation of the four indicators; RMSE represents the root mean square error between the measured value and the predicted value on the validation set; MAE represents the mean absolute error between the measured value and the predicted value on the validation set; R 2 Represents the coefficient of determination on the validation set; MAPE represents the mean absolute percentage error between the measured and predicted values on the validation set;

[0154] In the multi-index comprehensive scoring equation, RMSE accounts for 30% of the weight, MAE accounts for 30% of the weight, R 2 The weight is 20%, and the MAPE weight is 20%;

[0155] The multi-index comprehensive scoring equation scores the training results of the current parameter combination, where the total weight of RMSE, MAE and MAPE accounts for 80%, R 2 The weight of is 20%, and the smaller the score, the better the performance of the model;

[0156] (3) Based on the comprehensive score value obtained by the multi-index comprehensive scoring equation, the training parameters of the machine learning regression model are globally optimized in combination with grid search to obtain the optimal parameter combination of the model, including:

[0157] traversing preset parameter combinations through grid search, performing model training iterations on the training set, and quantitatively evaluating film thickness prediction performance based on the validation set;

[0158] Analyze the performance evaluation indicators of the model under each set of parameter combinations, and combine the comprehensive score to obtain the optimal parameter combination of the machine learning regression model;

[0159] Finally, the model score value A under each set of parameter combinations CNNAs a guide for optimal parameter selection, the optimal parameter combination of the CNN regression model was obtained: Learning_rate = 1e-3, Batch_size = 16, Epoch = 50, Optimizer = 'RMSporp', Weight_decay = 1e-4, Decay_rate = 0.999.

[0160] In the above step S3, the following contents are specifically included:

[0161] Based on the optimal parameter combination obtained above, model training is performed according to the training set and the validation set to obtain the optimal CNN model as the optimization model; the optical image of the film to be predicted in the test set is input into the optimization model to obtain the corresponding thickness prediction value;

[0162] (1) Model training, specifically including: setting the training parameters of the CNN regression model to the optimal parameter combination in step S2, i.e., Learning_rate = 1e-3, Batch_size = 16, Epoch = 50, Optimizer = 'RMSporp', Weight_decay = 1e-4, Decay_rate = 0.999, and then training the model based on the training set and the validation set to obtain the optimal CNN model as the optimized model;

[0163] (2) Model prediction, specifically including: inputting the optical image of the film to be predicted in the test set into the optimization model to obtain the corresponding film thickness prediction value.

[0164] like Figure 4 The figure shows the scatter plot of the thickness measured value and the thickness predicted value of the CNN model in the test set data in Example 3 and the visualization of the recognition results of 4 groups of typical samples. The MSE of the CNN model in the test set data is 0.0007, MAE is 0.0202, RMSE is 0.0265, MBE is 0.0002, R 2 =0.9915; Figure 4 Figure (a) shows the scatter plot of the measured thickness values and the predicted thickness values of the CNN model in the test set data; Figure 4 Figure (b) shows the visualization of the recognition results of four typical groups of samples. The measured thickness values are 70nm, 132nm, 140nm and 186nm, and the corresponding predicted thickness values are 69.30nm, 132.82nm, 139.91nm and 184.80nm, respectively. The coefficient of determination close to 1 and the low error value indicate the high accuracy of the CNN model in identifying the thickness of BaTiO3 films.

[0165] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A ferroelectric thin film thickness identification method based on a multi-index comprehensive scoring equation, characterized in that: include: Optical imaging equipment collects optical images of the ferroelectric thin film surface; Perform data preprocessing, data enhancement, and manual annotation on images to build a dataset system; Establish a system including root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R 2 ) and the mean absolute percentage error (MAPE) multi-index comprehensive scoring equation; Combined with grid search to globally optimize the training parameters of machine learning regression models; The obtained optimized model is used to predict the thickness of the image to be predicted.

2. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, wherein: The multi-index comprehensive scoring equation specifically includes: The formula of the multi-index comprehensive scoring equation is as follows: A=x×RMSE+y×MAE+z×R 2 +w×MAPE Among them, A is a comprehensive score obtained by weighted summation of the four indicators; RMSE represents the root mean square error between the measured value and the predicted value on the validation set; MAE represents the mean absolute error between the measured value and the predicted value on the validation set; R 2 Represents the coefficient of determination on the validation set; MAPE represents the mean absolute percentage error between the measured and predicted values on the validation set; In the multi-index comprehensive scoring equation, RMSE accounts for weight x, MAE accounts for weight y, R 2 Occupies weight z, MAPE occupies weight w; The range of the variable z is 0.2≤z≤0.7, and the total weight x+y+z+w=1.

3. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, wherein: The ferroelectric thin film is any one of BaTiO3, BiFeO3, PbTiO3, Pb(Zr, Ti)O3, and (Hf, Zr)O2, and has a thickness of 1-450 nm.

4. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, wherein: The optical imaging device collects an optical image of the surface of the ferroelectric thin film, specifically comprising: An optical microscope and a high-resolution camera are used to collect optical images of the surface of the ferroelectric thin film. The resolution of the obtained optical image is not less than 3840×2160 pixels, and the physical size of a single pixel is 2μm×2μm. According to the thickness information of the ferroelectric thin film, the collected optical images are classified to obtain a ferroelectric thin film optical image dataset.

5. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, wherein: The data preprocessing specifically includes: Data cleaning: remove duplicate and invalid images; Image normalization: The cleaned image resolution is uniformly converted to 512 × 512 pixels and normalized; Dataset division: The ferroelectric thin film optical image dataset obtained after the above processing is divided into a training optical image dataset, a verification optical image dataset, and a test optical image dataset.

6. The method for identifying the thickness of a ferroelectric film based on a multi-index comprehensive scoring equation according to claim 1, characterized in that Data enhancement processing, specifically including: Perform random rotation (angle range 0°≤θ≤180°), flip (horizontally / vertically), scaling and cropping (scaling ratio 0.8-1.2), and brightness perturbation (ΔL±15%) operations on the images in the training optical image dataset and the validation optical image dataset; The image size is then adjusted twice to ensure that the output image size is 224×224 pixels, and finally the training optical image enhancement dataset and the verification optical image enhancement dataset are obtained.

7. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, wherein: The manual annotation process specifically includes: According to the thickness information of the images in the training optical image enhancement dataset, the verification optical image enhancement dataset and the test optical image dataset, the images are manually annotated to obtain the dataset system, which includes a training set, a verification set and a test set.

8. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, wherein: The machine learning regression model specifically includes: The machine learning regression model is a convolutional neural network regression model; The convolutional neural network regression model adopts a three-level convolutional feature extraction architecture: the first feature extraction layer contains a 32-channel 3×3 convolution kernel and a 2×2 pooling layer; the second feature extraction layer is configured with a 64-channel 3×3 convolution kernel and a 2×2 pooling layer; the third feature extraction layer deploys a 128-channel 3×3 convolution kernel; the feature tensor is topologically converted from three-dimensional spatial features to one-dimensional vectors through the Flatten layer, and finally the feature space mapping is completed through a fully connected layer with 128 hidden units.

9. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, wherein: The grid search is combined to globally optimize the training parameters of the machine learning regression model, specifically including: traversing preset parameter combinations through grid search, performing model training iterations on the training set, and quantitatively evaluating film thickness prediction performance based on the validation set; Analyze the performance evaluation indicators of the model under each set of parameter combinations, and combine the comprehensive score value to obtain the optimal parameter combination of the machine learning regression model.

10. The method for identifying the thickness of a ferroelectric thin film based on a multi-index comprehensive scoring equation according to claim 1, characterized in that: The method of using the obtained optimization model to predict the thickness value of the image to be predicted specifically includes: Based on the optimal parameter combination, model training is performed according to the training set and the validation set to obtain an optimized model; The optical image of the film to be predicted in the test set is input into the optimization model to obtain the corresponding thickness prediction value.

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