Synthetic holographic mask rapid design method based on deep convolutional generative adversarial network

Abstract

The invention provides a rapid design method for a synthetic holographic lithography mask based on a deep convolutional generative adversarial network (DCGAN), and the method comprises the following steps: firstly, carrying out the extraction of the mask, and then, carrying out the extraction of the mask, and carrying out the extraction of the mask, and carrying out the extraction of the mask, the extraction of the mask, and the extraction of the mask. A mapping relation between a DCGAN learning target and a mask based on U-net is utilized, and a quasi-optimal synthetic holographic mask containing phase amplitude modulation is predicted through the trained generative network; and local optimization is carried out on the key area through a physical iteration method. According to the method, the convergence speed can be greatly improved, local optimum can be avoided, meanwhile, the high quality of a photoetching space image is kept, and the optimization effect is more remarkable especially for a large-size mask pattern.

Description

Technical Field

[0001] The present invention belongs to the technical field of holographic mask lithography, and particularly relates to a method for rapidly designing a synthetic holographic mask based on a deep convolution generative adversarial network (DCGAN). Background Art

[0002] Compared with the mainstream projection lithography technology, the synthetic holographic mask lithography technology has the characteristics of low cost and easy equipment maintenance, and can also achieve high yield. Compared with the traditional proximity lithography technology, the synthetic holographic mask lithography technology can achieve higher-resolution lithographic imaging without significant modification of the equipment or process, and has great industrial application potential.

[0003] The design of synthetic holographic masks usually adopts an iterative algorithm based on alternating projection. However, due to the limitations of the mask manufacturing process, the algorithm needs to discretize the continuous phase and amplitude distributions during the design process. In Prior Art 1 (Weichelt, T., et al. "Resolution enhancement for advanced mask alignerlithography using phase-shifting photomasks." Optics express 22.13 (2014): 16310-16321.), the Gerchberg-Saxton (GS) algorithm is used to calculate the amplitude and phase distributions of the holographic lithography mask of the target pattern, and the physical characteristics of the mask (such as etching depth) are used to regulate the phase. Prior Art 2 (Liu Yuyang, Li Sikun. Holographic lithography mask design method based on alternating projection algorithm. CN Patent202411800836.X. Feb 21, 2025.) proposes a holographic lithography mask design method based on the alternating projection algorithm, which can achieve higher-resolution pattern transfer compared with the traditional GS method and is suitable for the design of synthetic holographic masks for complex patterns. The synthetic holographic mask design methods in the above technologies are essentially a kind of inverse lithography or phase recovery, and the selection of the initial value of the algorithm has a significant impact on the result. An inappropriate initial value may cause the iterative algorithm to fall into a local optimal solution. In addition, in the problem of large-area synthetic holographic mask design, due to the discretization of the mask plane requiring a large number of iterations, the algorithm efficiency decreases.

[0004] With the development of artificial intelligence, deep learning has achieved remarkable results in the field of computational lithography. The prior art 3 (Yang H, Li S, Ma Y, et al. "GAN-OPC: Mask optimization with lithography-guided generative adversarial nets." Proceedings of the 55th Annual Design Automation Conference. 2018: 1-6.) applied the generative adversarial network to optical proximity effect correction. By constructing the mapping relationship between the target pattern and the pre-optimized mask structure, quasi-optimal mask generation was achieved, and the final optimization was completed by combining a small amount of traditional optimization algorithms. However, this technology lacks the processing of phase information and cannot be directly applied to the design of synthetic holographic masks. Summary of the Invention

[0005] To overcome the deficiencies of the above-mentioned prior art, the present invention provides a rapid design method for synthetic holographic masks based on a deep convolutional generative adversarial network (DCGAN), which is used to improve the design efficiency of synthetic holographic mask lithography technology, can effectively characterize and process the phase information of the mask plane, and is applicable to the rapid design of synthetic holographic masks. This method represents the synthetic holographic mask by pixels, and the value of each pixel is a complex value, which contains the phase and amplitude information of this point. A hybrid optimization architecture combining DCGAN pre-generation and physical iterative model refinement is constructed: First, use the DCGAN based on the U-net framework to learn the mapping relationship between the target pattern and the synthetic holographic mask, and generate a quasi-optimal synthetic holographic mask containing phase amplitude modulation; taking the quasi-optimal synthetic holographic mask as the initial value, then locally optimize the key areas through physical design methods. Compared with the traditional physical design method, the present invention can significantly improve the design efficiency and effectively avoid the optimization from falling into the global optimal solution.

[0006] The solution of the present invention is as follows:

[0007] Step 1. Prepare the dataset. Enlarge and crop the physical size represented by the mask image according to a specific ratio so that its size characteristics meet the resolution of synthetic holographic mask lithography;

[0008] Step 2. Preprocess the dataset. Use the binary mask of the target pattern as the initial amplitude of the wafer plane, and alternately phase-shift the polygon as the initial phase distribution. Propagate it back to the mask plane through the angular spectrum of plane waves (ASPW) algorithm, and the ungraded amplitude and phase distribution obtained are used as the input data z of the generation network. At the same time, calculate the true synthetic holographic mask corresponding to the target pattern based on the physical model and use it as the input y of the discriminant network;

[0009] Step 3. Build a deep convolutional generative adversarial network model based on PyTorch, including a generator network DN and a discriminator network GN, as Figure 1 shown;

[0010] Step 4. And use the preprocessed dataset to train the network, optimize the model parameters, and save the trained generator network model GN;

[0011] Step 5. Based on the trained generator network GN, build a fast design method for synthetic holographic masks, as Figure 2 shown. Input the preprocessed input z of the target pattern, and predict the corresponding quasi-optimal synthetic holographic mask G(z) through the generator network. Then input it into the physical design method as the input, and obtain the optimal synthetic holographic mask m after iterative optimization.

[0012] Step 6. Evaluate the quality of the synthetic holographic mask. Through the lithography imaging model, expose and image the designed synthetic holographic mask m to obtain the aerial image I wafer . Use the Sigmoid model to convert the aerial image into the photoresist profile and set the evaluation function D, where D is the value of the area error (Area Error Ratio, AER) of the photoresist profile in the calculation plane: where N is the total number of pixel points in the calculation area, ║*║ 2 represents the L-2 norm, and z target is the photoresist profile of the target pattern.

[0013] Furthermore, Step 3 includes the following steps:

[0014] Step 3.1. Build a generator network. The generator network consists of convolutional / transposed convolutional layers, normalization layers, Relu / LeakyRelu activation layers, and a final Tanh activation layer. Adopt a U-net-based structure to perform skip connections between the i-th layer and the n-i-th layer (n is the number of network layers) to fuse low-level and high-level information. During downsampling, use convolutional operations to increase the number of channels to extract feature information. And use the LeakyRelu activation function to avoid the problem of gradient disappearance in the negative half-axis. During upsampling, restore the spatial resolution and reduce the number of channels through transposed convolutional operations, and at the same time use Relu activation and random dropout to prevent overfitting. The finally output image is normalized to [-1, 1] by Tanh as the complex amplitude distribution of the output synthetic holographic mask;

[0015] Step 3.2. Construct the discriminant network. The discriminant network consists of a convolutional layer, a normalization layer, a Relu activation layer, a fully connected layer, and a final Sigmoid activation function. The network first extracts deep features through convolutional operations, then weights the features through the fully connected layer, and finally makes a judgment through the Sigmoid activation function to determine whether the input is a real synthetic holographic mask;

[0016] Furthermore, the steps of network training in Step 4 are as follows:

[0017] Step 4.1. Divide the dataset into small batches of data;

[0018] Step 4.2. Set the loss function. The loss function L of the discriminant network D is defined as:

[0019]

[0020] where y ∼ Holomask(y) means that y is taken from the data of the real synthetic holographic mask, z ∼ target(z) means that z is taken from the data containing the target graphic information, and E(*) represents the expected value. D(y) is the predicted value of the discriminant network for the real sample. The closer its value is to 1, the more effectively the discriminant network can distinguish that the input comes from the synthetic holographic mask generated by the physical design method, that is, the stronger the performance of the discriminant network.

[0021] The loss function of the generator network consists of the adversarial loss L G-adv and the content generation loss L G-gen jointly. The purpose of the adversarial loss L G-adv is to prompt the data generated by the generator network to "fool" the discriminant network. The content generation loss L G-gen mainly focuses on the similarity between the generated data and the real data in terms of content, and is determined by measuring the difference in distribution between the generated synthetic holographic mask G(z) and the real synthetic holographic mask y obtained by the physical design method. Their expressions are respectively:

[0022] L G-adv =-E z～target(z) [log[D(G(z))]]

[0023] L G-gen =E z～target(z) [||G(z)-y||1]

[0024] The loss function L of the generator network G is:

[0025] L G =L G-adv +λ0L G-gen

[0026] Among them, λ0 is a hyperparameter that balances the adversarial loss of attributes and the content generation loss;

[0027] Step 4.3. Set training parameters. Use the Adam optimization algorithm as the optimizer, set parameters such as Batchsize, maximum epoch, learning rate lr, etc., and set the saving strategy of the network structure;

[0028] Step 4.4. Network training. The input of the generation network is the preprocessed data, which contains target graphic information. The data undergoes feature extraction through convolutional layers in the network, and then the spatial resolution is restored through deconvolution, and finally the predicted synthetic holographic mask graphic G(z) is output. The amplitude and phase of this graphic will be appropriately graded according to the discretization strategy. Then, the synthetic holographic mask data G(z) predicted by the generation network and the real sample y generated by the physical design method are input into the discriminative network together. The discriminative network is trained to optimize the parameters of each layer. After the discriminative network training is completed, keep its network parameters unchanged, and backpropagate the training error to the generation network to update the parameters of each layer of the generation network. Subsequently, use the new synthetic holographic mask predicted by the updated generation network as the input data for the next round of training. Through the alternating training of the generation network and the discriminative network, until the preset number of iterations is reached, thus completing the training process of the entire network.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] Compared with the prior art 2, the present invention uses DCGAN to learn the mapping relationship between the target graphic and the synthetic holographic mask distribution. Through the trained model, the quasi-optimal synthetic holographic mask with discretized amplitude and phase can be directly generated according to the target graphic. Taking the quasi-optimal synthetic holographic mask as the initial value, input it into the physical design method for iterative calculation to obtain the optimal synthetic holographic mask distribution. The difference between the fast design method in the present invention and the design method in the prior art 2 is that it directly performs forward propagation with the quasi-optimal synthetic holographic mask as the initial value of the mask plane, without the need to backpropagate from the silicon wafer plane back to the mask plane. By combining the data-driven deep learning method with the traditional physical design model, not only the advantage of DCGAN in quickly generating data is utilized, but also the ability of the physical design model to accurately describe the actual physical process is retained. Compared with the traditional iterative algorithm, the present invention improves the iterative efficiency by optimizing the initial value, and at the same time, the obtained optimal synthetic holographic mask has high imaging quality. Description of the Drawings

[0031] Figure 1 is a schematic diagram of the deep convolutional generative adversarial network structure in the present invention

[0032] Figure 2It is the flowchart of the fast design method of synthetic holographic mask based on generative adversarial network in the present invention

[0033] Figure 3 It is the target pattern for designing the synthetic holographic lithography mask using the present invention

[0034] Figure 4 It is the aerial image and photoresist profile after exposure of the synthetic holographic lithography mask obtained by using the present invention

[0035] Figure 5 It is the iteration curve of mask design using the present invention and the existing technology respectively

[0036] Figure 6 It is the number of convergence times of synthetic holographic mask design for mask patterns of different sizes using the present invention and the existing technology respectively, and the performance of the photoresist AER after exposure Detailed implementation mode

[0037] To illustrate the present invention more clearly, the following will be described in detail with specific examples. It should be noted that these examples are only used to explain the implementation mode of the present invention and do not constitute a limitation on the scope of the present invention

[0038] In this example, the holographic lithography mask design method based on the alternating projection algorithm (i.e., prior art 2: Liu Yuyang, Li Sikun. Holographic lithography mask design method based on alternating projection algorithm. CN Patent 202411800836.X. Feb 21, 2025.) is used as the comparison object. The simulation uses some masks in the CAD2013 competition dataset as the target patterns, and uses the physical design method to generate the corresponding synthetic holographic masks to construct the training dataset. At the same time, the remaining mask patterns in the CAD2013 competition dataset are selected as the test set to evaluate the performance of the fast design method and the physical design method in terms of design efficiency and AER evaluation index

[0039] The flow of the embodiment of the present invention Figure 1 And Figure 2 As shown

[0040] Step 1. Select the masks in the ICCAD2013 competition dataset as the target patterns, with a total of 5394 samples. Since there is a difference between the physical size represented by the mask pictures of the original data and the lithography resolution adapted to holographic lithography, the original pictures need to be preprocessed. The physical size represented by the mask pictures is enlarged and cropped according to a specific ratio so that its size characteristics are more in line with the resolution of holographic lithography. After the preprocessing, the size of the calculation grid is 50μm × 50μm, the sampling interval is 0.1μm, the minimum graphic feature size in all samples is 2μm, and the maximum is 4μm

[0041] Step 2. Further preprocess the dataset in Step 1. Use the binary mask of the target pattern as the initial amplitude of the wafer plane, alternately shift the polygon to obtain the initial phase distribution, and backpropagate it to the mask plane through ASPW. The obtained ungraded amplitude and phase distribution are used as the input data z of the generation network. At the same time, establish a holographic lithography mask design method based on the alternating projection algorithm. Use the binary distribution of the target pattern as the initial amplitude distribution, and alternately shift some polygons as the initial phase distribution to generate the corresponding synthetic holographic mask y. Limited by mask manufacturing constraints, set the phase grading of the synthetic holographic mask to 0 and π, and the amplitude grading to 0 and 1. Among all the samples, 394 samples are selected as the test set, and the remaining 5000 samples are randomly divided into a training set and a validation set according to an 8:2 ratio during the training process.

[0042] Step 3. Build a deep convolutional generative adversarial network model based on pytorch.

[0043] Step 3.1. Build the generation network. The network consists of convolutional / transposed convolutional layers, normalization layers, Relu / LeakyRelu activation layers, and a final Tanh activation layer. Adopt a U-net-based structure to perform skip connections between the i-th layer and the n-i-th layer (n is the number of network layers) to fuse low-level and high-level information.

[0044] Step 3.2. Build the discriminator network. The discriminator network consists of convolutional layers, normalization layers, Relu activation layers, fully connected layers, and a final Sigmoid activation function.

[0045] The specific network frameworks of the generation network GN and the discriminator network DN are shown in Tables 1 and 2. Among them, I, O, K, P, and S represent the number of input channels, the number of output channels, the size of the convolutional kernel, the padding size, and the stride size respectively. BN represents the normalization operation, and Relu and LeakyRelu are activation functions. The input tensor in the generation network contains two channels, corresponding to the amplitude data and the initial phase data containing the target pattern information respectively. The output is a single-channel image, which is the complex amplitude distribution of the mask. For the discriminator network, its input contains two channels, namely the predicted synthetic holographic mask output by the generation network and the real synthetic holographic mask generated by the corresponding physical design method. During the model evaluation process, in order to adapt to mask patterns of different resolutions, mask data of different resolutions will be considered during training. Therefore, the number of input nodes of FC in FC1 in Table 2 will be adjusted accordingly with the change of the mask resolution.

[0046] Step 4. Use the preprocessed dataset to train the network and optimize the model parameters. Save the trained generation network model GN.

[0047] Step 4.1. Divide the dataset into small batch data.

[0048] Step 4.2. Set the loss function. The loss function L of the discriminative network D is as follows:

[0049]

[0050] The loss function of the generative network consists of the adversarial loss L G-adv and the content generation loss L G-gen jointly.

[0051] L G-adv = -E z～target(z) [log[D(G(z))]]

[0052] L G-gen = E z～target(z) [||G(z)-y||1]

[0053] The loss function L of the generative network G is as follows:

[0054] L G = L G-adv + λ0L G-gen

[0055] where λ0 is a hyperparameter that balances the attribute adversarial loss and the content generation loss, and is set to 100.

[0056] Step 4.3. Set the training parameters. Use Adam as the optimization algorithm, set the Batchsize to 16, the maximum number of epochs to 200, and save the network data every 10 epochs. Set the learning rate lr to 0.0002 for the first 100 epochs and 0.0001 for the last 100 epochs;

[0057] Step 4.4. Network training. The input of the generative network is the preprocessed data, which contains the target graphic information. The data undergoes feature extraction through convolutional layers in the network, and then the spatial resolution is restored through deconvolution. Finally, the predicted synthetic holographic mask distribution G(z) is output. The amplitude and phase of the graphic will be appropriately graded according to the discretization strategy. Then, the synthetic holographic mask data G(z) predicted by the generative network and the real sample y generated by the physical design method are input into the discriminative network together. Train the discriminative network to optimize the parameters of each layer. After the discriminative network is trained, keep its network parameters unchanged, and backpropagate the training error to the generative network to update the parameters of each layer of the generative network. Subsequently, use the new synthetic holographic mask predicted by the updated generative network as the input data for the next round of training. Through the alternating training of the generative network and the discriminative network, until the preset number of iterations is reached, thus completing the training process of the entire network.

[0058] Step 5. Based on the trained generation network model GN, a rapid design method for synthetic holographic masks is constructed, as shown in Figure 2 . The preprocessed data z corresponding to the target pattern is input, and prediction is performed through the generation network to obtain the quasi-optimal synthetic holographic mask G(z). This quasi-optimal synthetic holographic mask is then input into the physical design method as the initial input, and after iterative optimization, the final optimal synthetic holographic mask m is obtained.

[0059] Step 6. Evaluate the imaging quality of the designed synthetic holographic mask.

[0060] In this example, a circular light source with an illumination angle of 0.3° and a wavelength of 365 nm is used for exposure, and the adjacent pitch is set to 50 μm. A mask pattern in the test set is selected as the test pattern, as shown in Figure 3 . The aerial image and photoresist profile obtained by the rapid design method are shown in Figure 4 . The aerial image has good contrast. The AER values of the photoresist obtained after exposure of the synthetic holographic masks generated by these two methods are 3.9×10 -3 and 3.6×10 -3 respectively, and the imaging quality is good. Figure 5 shows the convergence curves of the rapid design method and the physical design method, represented by dot lines and square dot lines respectively. The rapid design method tends to converge at about 25 iterations, while the physical design method reaches convergence at the 140th iteration, significantly improving the convergence efficiency of mask design.

[0061] To verify the universality of the present invention for the design of synthetic holographic masks of different sizes, the physical size and feature size of the target pattern are kept unchanged, the sampling pitch of the mask is changed, and the dataset is re-acquired according to the physical design method. The mask sizes are set to 300×300, 400×400, 500×500, 600×600, 700×700, and at the same time, the number of FC input nodes of the fully connected layer FC1 is adjusted according to the mask size. 394 samples in the test set are simulated, and the performance of the rapid design method and the physical design method in terms of the number of convergence times and the AER value of the photoresist after exposure is compared. The final results are shown in Figure 6 . Figure 6 (a) and (b) respectively show the number of iterations required for the rapid design method and the physical design method to reach convergence, and (c) and (d) respectively show the AER values after exposure using the corresponding synthetic holographic masks. The results show that the number of convergence iterations of the rapid design method is significantly reduced compared with the physical model, and the AER values of most samples are less than 5×10 -3The gap between the results obtained by the rapid design method and those of the physical design method is small, and high-quality exposure aerial images can be achieved. As the mask size increases, the improvement effect of the rapid design method becomes more obvious. For example, for the synthesis holographic mask design with a size of 700×700, the median number of iterations using the rapid design method is 22, while the median number of iterations using the physical design method is 244, and the iteration efficiency is increased by 90.98%, greatly improving the synthesis holographic mask design efficiency of high-resolution mask patterns.

[0062] The above results are one of the examples with good effects of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0063] Table 1 Structure of the generation network

[0064]

[0065] Table 2 Structure of the discriminant network

[0066]

[0067]

Claims

1. A fast design method for synthetic holographic masks based on a deep convolutional generative adversarial network (DCGAN), characterized in that It includes the following steps: Step 1: Data preparation and preprocessing: Adjust the size of the target mask pattern according to the requirements of holographic lithography resolution; Step 2: Construct and train a deep convolutional generative adversarial network (DCGAN) model: It includes a generator network (GN) and a discriminator network (DN). Among them, the generator network uses a U-net architecture to fuse multi-level features, and the discriminator network is used to distinguish between the generated mask and the real mask; Step 3: Mask generation and optimization: Based on the trained DCGAN model, input the preprocessed data of the target pattern, and use the quasi-optimal mask output as the initial value, and perform local optimization through a physical iteration method to obtain the final mask; Step 4: Quality evaluation: Perform quality evaluation on the final mask, calculate the area error ratio (AER) of the photoresist profile, and evaluate the mask performance.

2. The rapid design method of a synthetic holographic mask based on a deep convolutional generative adversarial network (DCGAN) according to claim 1, characterized in that, The preprocessing in Step 1 specifically includes: Use the binary mask of the target pattern as the initial amplitude distribution on the silicon wafer plane; Adopt the polygon alternating phase shift method to generate the initial phase distribution; Backpropagate through the plane wave angular spectrum algorithm to obtain the ungraded amplitude and phase distribution on the mask plane.

3. The rapid design method of synthetic holographic mask based on deep convolutional generative adversarial network (DCGAN) according to claim 1, characterized in that Step 2: Construct and train a deep convolutional generative adversarial network (DCGAN) model, specifically including: S2.1 Network model construction: Based on the Pytorch framework, construct a generative adversarial network model, including a discriminator network (DN) and a generator network (GN); among them, the generator network uses a U-net architecture, which includes a downsampling module and an upsampling module; the downsampling consists of a convolutional layer, a batch normalization layer, and a LeakyReLU activation layer, and gradually increases the number of feature channels and reduces the spatial resolution through convolutional operations to extract high-level features of the target pattern information; the upsampling module consists of a transposed convolutional layer, a batch normalization layer, a ReLU activation layer, and skip connections, and fuses low-level and high-level features through skip connections, and finally outputs the complex amplitude distribution and normalizes it to [-1, 1] through Tanh; the discriminator network consists of a convolutional layer, a normalization layer, a Relu activation layer, a fully connected layer, and a Sigmoid activation function, extracts deep features through convolutional operations, and outputs the probability value that the sample is a real synthetic holographic mask after being weighted by the fully connected layer; S2.2 Loss function definition: The loss function L of the generation network G is as follows: L G = L G-adv + λ0L G-gen Among them, λ0 is a hyperparameter that balances the adversarial loss and the content generation loss; L G-adv is the adversarial loss, and L G-adv = -E z～target(z) [log[D(G(z))]], and L G-gen is the content generation loss, that is, the difference in distribution between the synthetic generated holographic mask G(z) and the real synthetic holographic mask y obtained by the physical design method L G-gen = E z～target(z) [||G(z) - y||1]; The loss function L of the discrimination network D is as follows: Among them, y~Holomask(y) means that y is taken from the data of the real synthetic holographic mask, z~target(z) means that z is taken from the data containing the target pattern information, and E(*) represents the expected value; D(y) is the predicted value of the discriminator network for the real sample, and the closer its value is to 1, the more effectively the discriminator network can distinguish that the input comes from the synthetic holographic mask generated by the physical design method, that is, the stronger the performance of the discriminator network; S2.3 Network training and optimization: - Divide the data set containing the target pattern information and the real synthetic holographic mask data set into small batches of data; - Adopt the Adam optimization algorithm, and set the batch size (Batch Size), the maximum number of iterations (Max Epoch), the learning rate (Learning Rate), and the network weight saving strategy; - Fix the parameters of the generation network, input the real sample y and the holographic mask G(z) into the discriminative network, and minimize L D Optimize the parameters of the discriminative network; - Fix the discriminant network parameters, backpropagate the training error between the holographic mask G(z) and the real sample y to the generator network, and update the generator network parameters by minimizing L G Update the generator network parameters; - Repeat the above steps until the preset number of iterations is reached to generate a synthetic holographic mask that meets the physical design constraints.

4. The rapid design method of a synthetic holographic mask based on a deep convolutional generative adversarial network (DCGAN) according to claim 1, characterized in that, The imaging quality assessment uses a lithographic imaging model to calculate the area error rate (AER) value of the photoresist profile, and the formula is: where N is the total number of pixels in the calculation region, ║*║ 2 represents the L-2 norm, and z target is the photoresist profile of the target pattern.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the method for quickly designing a synthetic holographic mask according to any one of claims 1-4.

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