Deep learning-based critical-size small-angle X-ray scattering data processing method

Abstract

The invention provides a deep learning-based critical-size small-angle X-ray scattering data processing method, which comprises the following steps of: generating simulation data based on a physical model, constructing an omega-qxz two-dimensional image, and pre-training and storing a neural network model by utilizing the simulation image; small-angle X-ray scattering experiment data of the sample is collected, an experiment omega-qxz two-dimensional image is constructed, and a neural network model is trained and fine-tuned by using a training method during testing; and outputting critical dimension parameters according to the experimental image by using the trained and fine-tuned neural network. According to the method, the neural network is used for processing the two-dimensional image data, the key size parameters of the sample are rapidly predicted from the scattering data obtained from the sample at a small number of rotation angles, scattering signals at different angles do not need to be reconstructed to form a two-dimensional image under a qx-qz coordinate system, the testing speed is increased, and the testing efficiency is improved. And the time consumption of sample testing and data processing is reduced.

Description

Technical Field

[0001] This invention relates to critical dimension measurement technology, and more specifically to a deep learning-based method for processing critical dimension small-angle X-ray scattering data, which is suitable for measuring the critical dimensions of nanogratings or nanofield-effect transistors. Background Technology

[0002] Existing key-size small-angle X-ray scattering (CD-SAXS) data processing methods often require acquiring scattering information from samples at different rotation angles, which involves a large number of rotation angles, and reconstructing the scattering signals from different angles into q. x -q z Two-dimensional image in coordinate system (q) x q is the in-plane scattering vector, reflecting the periodicity or orientation characteristics of the sample structure in the direction parallel to the incident X-rays and the sample surface (i.e., the in-plane direction); z The out-of-plane scattering vector reflects the periodicity or orientation characteristics of the sample structure in the direction perpendicular to the sample surface (i.e., the out-of-plane direction). Furthermore, background signal subtraction and initial angle calibration are required before the sliced ​​signals of the two-dimensional image can be fitted to obtain the desired key dimensions.

[0003] The drawback of existing technology is that it requires testing images at multiple test angles to reconstruct two-dimensional images from scattering signals at different angles. Furthermore, considering the need for initial angle calibration and background subtraction, the testing of samples and data processing is time-consuming. Summary of the Invention

[0004] The purpose of this invention is to provide a key-size small-angle X-ray scattering data processing method based on deep learning to improve testing speed.

[0005] To achieve the above objectives, this invention provides a deep learning-based method for processing key-size small-angle X-ray scattering data, comprising:

[0006] S2: Generate simulation data based on the physical model, and use the simulation data to construct the simulation's ω–q. xz Two-dimensional image, using simulated ω–q xz Two-dimensional images are used to pre-train and save the neural network model, where ω is the rotation angle of the sample, and q... xz It is the scattering vector, ω–q xz Sample rotation angle - scattering vector;

[0007] S3: Collect small-angle X-ray scattering experimental data for the sample and construct the experimental ω–q using the experimental data. xz Two-dimensional images, using the test-time training method and experimental ω–q xzTwo-dimensional images are used to train and fine-tune neural network models.

[0008] S4: Using a trained and fine-tuned neural network model to study the ω–q of the experiment. xz The parameters of the sample are inverted by performing parameter inversion on the two-dimensional image, and the key size parameters of the sample are output.

[0009] Generate simulation data and use the simulation data to construct the simulation's ω–q. xz Two-dimensional images, specifically including: using a physical model of X-ray scattering, generating a large amount of simulation data corresponding to each set of key size parameters within the parameter space of key size parameters, and then constructing an ω–q image. xz image.

[0010] The sample is a nanograting, a periodic nanostructure, a nanofield-effect transistor, or a nanochip.

[0011] In step S3, small-angle X-ray scattering experimental data are collected from the sample within a specified rotation angle range; the specified rotation angle range can be any angle range, preferably a combination of three or more symmetrically distributed rotation angles within the range of -40° to +40°.

[0012] Using simulated ω–q xz Pre-training a neural network model using two-dimensional images specifically includes:

[0013] A1: For the simulation of ω–q xz Two-dimensional images undergo image preprocessing; the preprocessing includes: extracting simulated ω–q within a specified rotation angle range. xz Two-dimensional image; then all simulated ω–q xz Two-dimensional images are normalized to a uniform size;

[0014] A2: Establish a neural network model, which is used to convert ω–q xz Two-dimensional image regression is performed using multiple continuous key size parameters; ω–q is then used in the simulation. xz The neural network model is pre-trained using two-dimensional images.

[0015] Experimental data were collected for the sample within a specified rotation angle range, and the experimental data were used to construct the experimental ω–q. xz Two-dimensional images, specifically including: acquiring small-angle X-ray scattering data of the sample within a specified rotation angle range; subsequently, normalizing the data to the simulated ω–q. xz ω–q of experiments with uniform two-dimensional image sizes xz Two-dimensional image.

[0016] Experimental data were collected for the sample within a specified rotation angle range, and the experimental data were used to construct the experimental ω–q. xzTwo-dimensional images, also including: ω–q of the experiment xz The two-dimensional image itself is rotated and used as the input sample; during fine-tuning training, the rotation angle of the image is used as a pseudo-label, and the output of the neural network model is matched with the pseudo-label through model fine-tuning.

[0017] The neural network model is ResNet-34; during the training and fine-tuning process, only the parameters of the fully connected layers at the end of ResNet-34 are fine-tuned, while the rest of ResNet-34 is frozen.

[0018] The process of training and fine-tuning the neural network model also includes: introducing upper and lower limit constraints on key size parameters.

[0019] Before step S2, step S1 is also included: defining ω–q xz The data structure of a two-dimensional image, where ω is the rotation angle of the sample, and q xz It is the scattering vector; ω–q xz The vertical axis of the two-dimensional image is the scattering vector q. xz The modulus is denoted by q, the horizontal axis represents the sample rotation angle ω, and the pixel value is the corresponding scattering intensity intensity(q). xz );

[0020] In step S2, the scattering intensity (q) simulated at the rotation angle ω of each sample is used. xz ) is represented as a one-dimensional array (q) xz intensity(q) xz This leads to the one-dimensional array (q) xz intensity(q) xz The result of stacking the samples according to their rotation angle ω is used as the ω–q of the constructed simulation. xz Two-dimensional image.

[0021] The key-size small-angle X-ray scattering data processing method of the present invention, based on deep learning, uses a neural network model to process two-dimensional image data. This method is used to quickly predict key-size parameters of a sample from scattering data obtained at a small number of rotation angles, without needing to reconstruct q from scattering signals at different angles. x -q z Two-dimensional images in a coordinate system improve testing speed; no need for initial angle calibration or background subtraction, reducing the time spent on test samples and data processing. Attached Figure Description

[0022] Figure 1 This is a flowchart of a key-size small-angle X-ray scattering data processing method based on deep learning according to an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram of the key size parameters of the nanograting.

[0024] Figure 3 It is ω–q xz A schematic diagram of a two-dimensional image. Detailed Implementation

[0025] The present invention will be further described below with reference to specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0026] This invention proposes a deep learning-based method for processing critical size small-angle X-ray scattering data, primarily used to rapidly predict critical size parameters from scattering data obtained from samples at a small number of rotation angles. For example... Figure 1 As shown, the key-size small-angle X-ray scattering data processing method based on deep learning includes the following steps:

[0027] Step S1: Define ω–q xz The data structure of a two-dimensional image, where ω is the rotation angle of the sample, and q xz It is the scattering vector;

[0028] Where, ω–q xz The vertical axis of the two-dimensional image (i.e., the "sample rotation angle - scattering vector" two-dimensional image) is the scattering vector q. xz The modulus is denoted by q, the horizontal axis represents the sample rotation angle ω, and the pixel value is the corresponding scattering intensity intensity(q). xz ), rotation angle ω, scattering vector q xz Scattering intensity (q) xz ) constitutes the corresponding ω–q xz Scattering data set (ω,q) of data points on a two-dimensional image xz intensity(q) xz In this invention, the sample size information needs to be obtained by analyzing ω–q. xz Two-dimensional images are identified (the traditional method is to obtain ω–q). xz q is obtained by fitting data from a two-dimensional image. x and q z Theoretically speaking, q x =q xz ×cosω,q z =q xz ×sinω. It should be noted that q x -q z Two-dimensional images in a coordinate system have actual physical meaning, but the ω–q of this invention… xzTwo-dimensional images are constructed directly from experimental results and do not have a clear physical meaning.

[0029] Step S2: Generate simulation data based on the physical model, and use the simulation data to construct the simulation's ω–q. xz Two-dimensional image (i.e., simulated image of "sample rotation angle - scattering vector"), using simulated ω–q xz Two-dimensional images are used to pre-train and save neural network models;

[0030] As mentioned above, the simulation of ω–q xz The vertical axis of the two-dimensional image is the scattering vector q. xz The modulus is denoted by q, the horizontal axis represents the sample rotation angle ω, and the pixel value is the corresponding scattering intensity intensity(q). xz Therefore, in step S2, the scattering intensity intensity(q) simulated at the rotation angle ω of each sample is used. xz ) is represented as a one-dimensional array (q) xz intensity(q) xz This leads to the one-dimensional array (q) xz intensity(q) xz The result of stacking the samples according to their rotation angle ω is used as the ω–q of the constructed simulation. xz Two-dimensional images, thus avoiding the reconstruction of q in traditional methods x -q z The complex process of planarity.

[0031] In this embodiment, simulation data is generated, and the simulation data is used to construct the simulated ω–q. xz Two-dimensional images, specifically including: using a physical model of X-ray scattering, generating a large amount of simulation data corresponding to each set of key size parameters within the parameter space of key size parameters, and then constructing an ω–q image. xz Image. The simulation data is a scattering data set (ω, q). xz intensity(q) xz )).

[0032] In this embodiment, the constructed simulated ω–q xz A two-dimensional image is an image whose rotation angle ω is in the range of -40° to +40°, such as... Figure 3 As shown. Furthermore, the rotation angle increment for generating the simulation data is 1°.

[0033] The simulation data is specifically generated using a physical model of X-ray scattering, as follows:

[0034]

[0035] Where Af(q) xz ) is the scattering amplitude; I f (q xz ) is the scattering intensity; I(q) xz ) represents the scattering intensity after considering the Debye-Watson factor; σ is the scattering intensity. DWF It is the Debye-Watson factor; Σ T The total scattering cross section is represented by A; the integration range is A; ρ(r) is the density distribution, and r is the position vector; δ(x-nL) is the Dirac delta function, representing the scattering peak at x = nL, where n is the series number and L is the period; exp(-iq xz r) is the phase factor; q xz It is the scattering vector.

[0036] In this embodiment, as Figure 2 As shown, the sample is a nanograting; therefore, the key dimensional parameters include the period pitch, linewidth, height, and sidewall angle θ. In other embodiments, the sample may also be a nanofield-effect transistor, a nanochip, or other nanodevices, and the key dimensional parameters will vary accordingly.

[0037] Using the simulated ω–q xz During the pre-training of neural network models using two-dimensional images, key size parameters (i.e., pitch, width, height, θ) are used as labels.

[0038] Using simulated ω–q xz Pre-training a neural network model using two-dimensional images specifically includes:

[0039] Step A1: For the simulation of ω–q xz Image preprocessing for two-dimensional images;

[0040] The preprocessing includes: extracting ω–q from the simulation within a specified rotation angle range. xz Two-dimensional image; then all simulated ω–q xz The two-dimensional image is normalized to a uniform size (e.g., 224×224). In this embodiment, the uniform size is achieved by filling missing data with zeros; 224×224 represents q... xz Dimension and ω dimension.

[0041] As mentioned above, the constructed simulation ω–q xz The two-dimensional image is a rotation angle ω in the range of -40° to +40°. After normalization, the normalized image has valid data within the specified rotation angle range and zero-filled data in the remaining areas. This specified rotation angle range is consistent with the specified rotation angle range of the experimental data below.

[0042] Step A2: Establish a neural network model, which is used to convert ω–q xz Two-dimensional image regression is performed using four continuous key size parameters: pitch, width, height, and θ; using simulated ω–q xz The neural network model is pre-trained using two-dimensional images.

[0043] Specifically, the neural network model includes ResNet-34 as the backbone network. Therefore, the neural network model first uses convolutional layers of ResNet-34 to process ω–q. xz The image is convolved, and the resulting array vectors are connected to the four key size parameters pitch, width, height, and θ through a fully connected layer at the end of ResNet-34.

[0044] Using simulated ω–q xz Training the neural network model using two-dimensional images includes: based on simulated ω–q... xz Two-dimensional images are used to obtain corresponding predicted label values ​​and data label values. The mean square error (MSE) of four key size parameters (i.e., the mean square error between the predicted label value and the data label value) is used as the loss function. The model is trained for about 1000 rounds on a GPU server, enabling the neural network model to accurately learn the mapping relationship between the scattering map and the structural parameters from the simulation data.

[0045] Step S3: Collect small-angle X-ray scattering experimental data for the sample within a specified rotation angle range, and construct the experimental ω–q using the experimental data. xz Two-dimensional images (i.e., experimental images of "sample rotation angle - scattering vector") are obtained using test-time training (TTT) and experimental ω–q. xz Two-dimensional images are used to train and fine-tune neural network models.

[0046] Experimental data were collected for the sample within a specified rotation angle range, and the experimental data were used to construct the experimental ω–q. xz Two-dimensional images, specifically including: acquiring small-angle X-ray scattering data of samples (such as nanogratings, periodic nanostructures, nanofield-effect transistors, or nanochips) within a specified rotation angle range; subsequently, normalizing the data to obtain the simulated ω–q. xz ω–q of experiments with uniform two-dimensional image sizes xz Two-dimensional image (i.e., an image that has been filled with zeros and processed to be 224×224).

[0047] The purpose of test-time training (TTT) is to provide a shared feature extractor, feeding features from real-world data into a trained neural network model for fine-tuning. Experimental data is collected for samples within a specified range of rotation angles, and this data is used to construct the experimental ω–q... xz Two-dimensional images, also including: ω–q of the experiment xz The 2D image itself is rotated and used as the input sample; during fine-tuning training, the rotation angle of the image is used as a pseudo-label, and the output of the neural network model is matched with the pseudo-label through model fine-tuning. This is more conducive to learning the global features of the experimental data images.

[0048] In this embodiment, the specified rotation angle range is ±1°. Since the step size of the rotation angle for collecting experimental data is 1°, only data for three rotation angles—-1°, 0°, and 1°—need to be measured within the ±1° range. In other embodiments, the specified rotation angle range can be a combination of three or more symmetrically distributed rotation angles within the range of -40° to +40°, such as -1° to +1°, -5° to +5°, -15° to +15°, etc.

[0049] Furthermore, to enhance the model's adaptability to differences between experiments and simulations, during training fine-tuning, only the parameters of the fully connected layers at the ends of the ResNet-34 were fine-tuned, while the rest of the ResNet-34 was frozen. This allows for rapid optimization using small batches of experimental images, improving the prediction accuracy for specific samples.

[0050] The fine-tuning of neural network models can also include introducing upper and lower limits for key size parameters to prevent the neural network model from outputting unreasonable values. This can accelerate the training process. Introducing upper and lower limits for key size parameters can be achieved by setting penalties in the loss function, etc.

[0051] Step S4: Use the trained and fine-tuned neural network model to analyze the experimental ω–q. xz The parameters of the sample are inverted by performing parameter inversion on the two-dimensional image, and the key size parameters of the sample are output.

[0052] In this embodiment, the test performance of the present invention and the conventional method on different samples is compared, as shown in Table 1.

[0053] Table 1: Test performance of the present invention and traditional methods on different samples

[0054] The results show that, while maintaining accuracy, the method of the present invention increases the testing speed by about 50 times and significantly reduces the complexity of manual data processing.

[0055] This invention employs an image regression method, using a neural network model (ResNet-34) to process two-dimensional image data. This allows for the rapid prediction of key size parameters from scattering data obtained at a small number of rotation angles, without needing to reconstruct q from scattering signals at different angles. x -q z Two-dimensional images in a coordinate system improve testing speed; no initial angle calibration or background subtraction is required, reducing the time spent on test samples and data processing. Preliminary testing can significantly reduce the overall time compared to traditional methods (approximately 1 / 50th of the traditional method).

[0056] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. All simple and equivalent changes and modifications made in accordance with the claims and description of this application fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. A method for processing key-size small-angle X-ray scattering data based on deep learning, characterized in that, include: Step S2: Generate simulation data based on the physical model, and use the simulation data to construct the simulation's ω–q. xz Two-dimensional image, using simulated ω–q xz Two-dimensional images are used to pre-train and save the neural network model, where ω is the rotation angle of the sample, and q... xz It is the scattering vector, ω–q xz Sample rotation angle - scattering vector; Step S3: Collect small-angle X-ray scattering experimental data for the sample, and construct the experimental ω–q using the experimental data. xz Two-dimensional images, using the test-time training method and experimental ω–q xz Two-dimensional images are used to train and fine-tune neural network models. Step S4: Use the trained and fine-tuned neural network model to analyze the experimental ω–q. xz The parameters of the sample are inverted by performing parameter inversion on the two-dimensional image, and the key size parameters of the sample are output.

2. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 1, characterized in that, Generate simulation data and use the simulation data to construct the simulation's ω–q. xz Two-dimensional images, specifically including: using a physical model of X-ray scattering, generating a large amount of simulation data corresponding to each set of key size parameters within the parameter space of key size parameters, and then constructing an ω–q image. xz image.

3. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 1, characterized in that, The sample is a nanograting, a periodic nanostructure, a nanofield-effect transistor, or a nanochip.

4. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 1, characterized in that, In step S3, small-angle X-ray scattering experimental data are collected from the sample within a specified rotation angle range; the specified rotation angle range is a combination of three or more symmetrically distributed rotation angles within the range of -40° to +40°.

5. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 4, characterized in that, Using simulated ω–q xz Pre-training a neural network model using two-dimensional images specifically includes: Step A1: For the simulation of ω–q xz Two-dimensional images undergo image preprocessing; the preprocessing includes: extracting simulated ω–q within a specified rotation angle range. xz Two-dimensional image; then all simulated ω–q xz Two-dimensional images are normalized to a uniform size; Step A2: Establish a neural network model, which is used to convert ω–q xz Two-dimensional image regression is performed using multiple continuous key size parameters; ω–q is then used in the simulation. xz The neural network model is pre-trained using two-dimensional images.

6. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 5, characterized in that, Experimental data were collected for the sample within a specified rotation angle range, and the experimental data were used to construct the experimental ω–q. xz Two-dimensional images, specifically including: acquiring small-angle X-ray scattering data of the sample within a specified rotation angle range; subsequently, normalizing the data to the simulated ω–q. xz ω–q of experiments with uniform two-dimensional image sizes xz Two-dimensional image.

7. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 1, characterized in that, Experimental data were collected for the sample within a specified rotation angle range, and the experimental data were used to construct the experimental ω–q. xz Two-dimensional images, also including: ω–q of the experiment xz The two-dimensional image itself is rotated and used as an input sample; During fine-tuning training, the rotation angle of the image is used as a pseudo-label, and the output of the neural network model is matched with the pseudo-label through model fine-tuning.

8. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 1, characterized in that, The neural network model is ResNet-34; during the training and fine-tuning process, only the parameters of the fully connected layers at the end of ResNet-34 are fine-tuned, while the rest of ResNet-34 is frozen.

9. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 1, characterized in that, The process of training and fine-tuning the neural network model also includes: introducing upper and lower limit constraints on key size parameters.

10. The method for processing key-size small-angle X-ray scattering data based on deep learning according to claim 1, characterized in that, Before step S2, step S1 is also included: defining ω–q xz The data structure of a two-dimensional image, where ω is the rotation angle of the sample, and q xz It is the scattering vector; ω–q xz The vertical axis of the two-dimensional image is the scattering vector q. xz The modulus is given, the horizontal axis represents the sample rotation angle ω, and the pixel value is the scattering vector q. xz The corresponding scattering intensity (q) xz ); In step S2, the scattering intensity (q) simulated at the rotation angle ω of each sample is used. xz ) is represented as a one-dimensional array (q) xz intensity(q) xz This leads to the one-dimensional array (q) xz intensity(q) xz The result of stacking the samples according to their rotation angle ω is used as the ω–q of the constructed simulation. xz Two-dimensional image.

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