SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 2: Comparison on Lithography Simulation
Subtask	LithoGAN [22]	DAMO [12]	DOINN [23]	CFNO [16]
MSE_A	MSE_P	IOU	PA	MSE_A	MSE_P	IOU	PA	MSE_A	MSE_P	IOU	PA	MSE_A	MSE_P	IOU	PA
1	9.8·10-4	1.7·10-2	0.38	0.43	8.4·10-6	7.5·10-4	0.97	0.98	8.5·10-6	6.6·10-4	0.97	0.98	1.9·10-5	1.5·10-3	0.94	0.97
2	2.6·10-4	1.4·10-3	0.47	0.53	3.0·10-6	1.5·10-4	0.94	0.96	1.9·10-6	1.0·10-4	0.96	0.98	3.8·10-6	2.1·10-4	0.92	0.96
3	1.4·10-3	2.6·10-2	0.30	0.34	2.5·10-5	1.5·10-3	0.95	0.97	1.8·10-5	1.2·10-3	0.96	0.98	2.6·10-5	2.3·10-3	0.93	0.96
4	2.7·10-3	1.2·10-2	0.01	0.01	4.6·10-5	1.6·10-3	0.87	0.93	2.4·10-5	1.3·10-3	0.90	0.94	2.1·10-5	2.2·10-3	0.83	0.90
Average	1.3·10-3	1.4·10-2	0.29	0.33	2.1·10-5	1.0·10-3	0.93	0.96	1.3·10-5	8.2·10-4	0.95	0.97	1.7·10-5	1.5·10-3	0.91	0.95
Runtime	0.013 s / image	0.030 s / image	0.017 s / image	0.035 s / image
(a)
Figure 4: Lithography simulation. (a)Ground truth,(b)LithoGAN,(c)DAMO,(d)DOINN,(e)CFNO.
3. As shown in Fig. 3c, edge placement error (EPE) estimates the distortion of the resist image. We sample probe points equidistantly on horizontal and vertical edges of the target patterns. If the distance from the target pattern to the printed pattern is larger than the EPE constraint, it produces an EPE violation. The number of EPE violations is the EPE score of the mask.
4. Shot count (#Shots) is the number of rectangular shots for replicating the shapes on the mask. It can evaluate the complexity of an optimized mask. Fig. 3d shows an example, where a shape is fitted by rectangular shots. In LithoBench, we compute the shot count using adaptive rectangular decomposition [53] with adaptive-boxes [54] (MIT license).
Table 1 summarizes the statistics of LithoBench.
4.1 Benchmarked Models
4.1.1 Lithography Simulation Models
Multiple SOTA models are implemented using PyTorch [55] and OpenILT [56] on RTX3090 GPU. For lithography simulation, we implement LithoGAN [22], DAMO [12], DOINN [23], and CFNO [16]. The last layer of each model outputs two channels as the aerial and printed images. These models minimize the MSE between their outputs and the ground truths.
LithoGAN A CGAN is employed to fit the reference lithography simulation model. The generator of the CGAN is a fully convolutional network (FCN) [57] and the discriminator is a convolutional neural network (CNN). Images are downsampled to  $256 \times 256$  and input to the model. Note that different models may vary in image resolution to make trade-offs between accuracy and runtime.
Table 3: Comparison on Mask Optimization
Subtask	GAN-OPC [9]	Neural-ILT [11]	DAMO [12]	CFNO [16]
\( L_2 \)	PVB	EPE	Shots	\( L_2 \)	PVB	EPE	Shots	\( L_2 \)	PVB	EPE	Shots	\( L_2 \)	PVB	EPE	Shots
1	43414	41290	8.7	574	36670	42666	7.3	476	32579	41173	5.4	523	47814	46131	12.5	302
2	14767	6686	8.3	166	12723	8537	6.2	263	5081	9962	0.0	176	8949	9890	0.1	184
3	25929	23715	4.6	457	20045	23548	2.4	373	16120	23796	0.2	418	26809	26814	4.2	232
4	81378	4931	73.2	276	25422	41537	3.2	265	50445	35673	26.7	458	70740	17950	55.1	396
Average	41372	19156	23.7	368	23715	29072	4.8	344	26056	27651	8.0	394	38578	25196	18.0	279
Runtime	0.010 s / image	0.025 s / image	0.028 s / image	0.040 s / image
(b)
Figure 5: Mask optimization. (a)Ground truth,(b)GAN-OPC,(c)Neural-ILT,(d)DAMO,(e)CFNO.
DAMO It improves the CGAN for lithography simulation with the backbone based on UNet++ [58] and the multiscale discriminator inspired by pix2pixHD [59]. The resolution of DAMO is  $1024 \times 1024$ , which is significantly higher than LithoGAN.
DOINN Inspired by Fourier Neural Operator (FNO) [60], DOINN utilizes a novel reduced FNO architecture to fit the lithography simulation model. Its resolution is  $1024 \times 1024$ .
CFNO Combining the principles of Vision Transformer (ViT) [45] and FNO, the CFNO module is designed for efficient global layout embedding and resolving stitching issues caused by long-range dependency. The resolution for CFNO is also  $1024 \times 1024$ .
4.1.2 Mask Optimization Models
For mask optimization, we implement GAN-OPC [9], Neural-ILT [11], DAMO [12], and CFNO [16].
GAN-OPC CGAN also inspires the design of GAN-OPC. The training of GAN-OPC consists of two stages. In the first stage called ILT-guided pretraining, we train the generator to minimize the MSE between its outputs and the optimized masks. The second stage is based on the training process of GAN. During the training of the generator, we use the L2 loss formulated by (5) as an additional objective, where the printed image  $Z_{nom}$  is obtained by the reference lithography simulation model. GAN-OPC uses a resolution of  $256 \times 256$ .
Neural-ILT A UNet [61] is utilized in Neural-ILT to predict the optimized mask. Neural-ILT also has a pretraining stage like GAN-OPC. In the second stage, it uses  $L2(Z_{nom}, T) + PVB(Z_{max}, Z_{min})$  as the objective function. The resolution of Neural-ILT is  $512 \times 512$ .
DAMO and CFNO use the same architectures as in lithography simulation.
4.1.3 Subtasks
For lithography simulation and mask optimization, we benchmark the models with the following subtask: (1) training on MetalSet, testing on MetalSet; (2) training on ViaSet, testing on ViaSet; (3) training on MetalSet, testing on StdMetal; (4) training on ViaSet, testing on StdContact. The last two are more challenging since high generalization ability is required in these subtasks.
4.2 Results on Lithograph Simulation
Table 2 presents the performance of the tested models on all subtasks.  $\mathrm{MSE}_A$  and  $\mathrm{MSE}_P$  are the MSE losses of the aerial and printed images. Fig. 4 shows the outputs images of the models. DOINN achieves the best performance with a competitive runtime. DAMO and CFNO have comparable performance, which is beyond the reach of LithoGAN. As shown in Fig. 4b, even a coarse generation of the target shapes is too difficult for LithoGAN. This can be explained by two factors. First, LithoGAN
uses a lower resolution than other methods, which makes it harder for LithoGAN to approximate the shapes in a higher resolution. Second, the convolution layers in LithoGAN progressively shrink the feature maps until they reach a size of  $512 \times 1 \times 1$  at the intermediate layer. Since the printed image resembles the input mask, it is difficult to decode the complex shapes from such low-resolution feature maps. Thus, high-resolution features and outputs are essential for accurate lithography simulation.
4.3 Results on Mask Optimization
Table 3 compares the mask optimization models on all subtasks. Fig. 5 shows the output masks of the models. While GAN-OPC has the best PVB among these methods, it sacrifices L2 and EPE. It fails to learn the complicated curves that improve the L2 loss due to its low resolution. With a moderate resolution, Neural-ILT achieves moderate performance on the first three tasks. But it generalizes well to StdContact, enabling it to achieve the best average L2 and EPE. DAMO has the best performance on the first three tasks, while CFNO achieves lower mask complexity due to the small shot counts. In mask optimization, the model designer may consider the trade-off between resolution, generalization, and complexity. It is challenging to design a model that is optimal across all metrics.
In this paper, we present LithoBench, a dataset for DNN-based lithography simulation and mask optimization with an evaluation platform. LithoBench includes 133,496 layout tiles that involve the metal and via layers of circuit layouts. It can not only support the typical setup where a model is trained and evaluated on similar tiles, but also evaluate the model's generalization ability to unseen data. Given the data, state-of-the-art DNN models for lithography simulation and mask optimization are trained and evaluated on LithoBench to show their advantages and weaknesses. We hope LithoBench can contribute to the further development of computational lithography.
[1] C. Mack, Fundamental principles of optical lithography: the science of microfabrication. John Wiley & Sons, 2007.
[2] J.-S. Park et al., "An efficient rule-based opc approach using a drc tool for 0.18/spl mu/m asic," in IEEE International Symposium on Quality Electronic Design (ISQED), 2000, pp. 81-85.
[3] A. Awad et al., "A fast process variation and pattern fidelity aware mask optimization algorithm," in IEEE/ACM International Conference on Computer-Aided Design (ICCAD), 2014, pp. 238-245.
[4] J. Kuang, W.-K. Chow, and E. F. Young, "A robust approach for process variation aware mask optimization," in IEEE/ACM Proceedings Design, Automation and Test in Eurpoe (DATE), 2015, pp. 1591-1594.
[5] Y.-H. Su et al., "Fast lithographic mask optimization considering process variation," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), vol. 35, no. 8, pp. 1345-1357, 2016.
[6] Y. Liu et al., "Inverse lithography technology principles in practice: Unintuitive patterns," in BACUS Symposium on Photomask Technology, vol. 5992, 2005, pp. 886-893.
[7] J.-R. Gao et al., “MOSAIC: Mask optimizing solution with process window aware inverse correction,” in ACM/IEEE Design Automation Conference (DAC), 2014.
[8] Z. Yu et al., "A GPU-enabled level-set method for mask optimization," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), vol. 42, no. 2, pp. 594-605, 2022.
[9] H. Yang et al., "GAN-OPC: Mask optimization with lithography-guided generative adversarial nets," in ACM/IEEE Design Automation Conference (DAC), 2018.
[10] ——, “GAN-OPC: Mask optimization with lithography-guided generative adversarial nets,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), vol. 39, no. 10, pp. 2822–2834, 2019.
[56] S. Zheng, B. Yu, and M. Wong, "OpenILT: An open source inverse lithography technique framework," in IEEE International Conference on ASIC (ASICON), 2023.
[57] J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 3431–3440.
[58] Z. Zhou et al., "Unet++: A nested u-net architecture for medical image segmentation," in Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, 2018, pp. 3-11.
[59] T.-C. Wang et al., "High-resolution image synthesis and semantic manipulation with conditional GANs," in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018, pp. 8798-8807.
[60] Z. Li et al., “Fourier neural operator for parametric partial differential equations,” in International Conference on Learning Representations (ICLR), 2020.
[61] O. Ronneberger, P. Fischer, and T. Brox, "U-net: Convolutional networks for biomedical image segmentation," in International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), 2015, pp. 234-241.