MorphOPC: Advancing Mask Optimization with Multi-scale Hierarchical Morphological Learning

Yuting Hu; Lei Zhuang; Chen Wang; Ruiyang Qin; Hua Xiang; Gi-joon Nam; Jinjun Xiong

cs.CVApr 13, 2026

MorphOPC: Advancing Mask Optimization with Multi-scale Hierarchical Morphological Learning

Authors: Yuting Hu, Lei Zhuang, Chen Wang, Ruiyang Qin, Hua Xiang, Gi-joon Nam, Jinjun Xiong

Organizations: University at Buffalo, Buffalo, NY, USA · IBM T. J. Watson Research Center, Yorktown Heights, NY, USA · Villanova University, Villanova, PA, USA

Abstract

As feature sizes shrink to the nanometer scale, accurately transferring circuit patterns from photomasks to silicon wafers becomes increasingly challenging. Optical proximity correction (OPC) is widely used to ensure pattern fidelity and manufacturability. Recent generative mask optimization models based on encoder-decoder architecture can synthesize near-optimal masks, serving as fast machine learning (ML) surrogates for traditional OPC. However, these models often fail to capture the geometric transformations from target layouts to mask patterns, leading to suboptimal quality. In this work, we formulate mask generation as a sequence of morphological operations on local layout features and propose MorphOPC, a multi-scale hierarchical model with neural morphological modules to learn these transformations. Experiments on edge-based OPC and ILT benchmarks across metal and via layers show that MorphOPC consistently outperforms state-of-the-art methods, achieving higher printing fidelity and lower manufacturing cost, demonstrating strong potential for scalable mask optimization.

Figures & tables

Figure 1. (a) MorphOPC learns morphological operations on local features for mask generation. (b) MorphOPC supports both pixel-based (ILT) and edge-based (EBOPC) OPC across metal and via layers.

Figure 2. Illustration of MorphOPC architecture.

Figure 3. Views of morphological outputs relative to the input convolutional feature maps at (a) layer-2 and (b) layer-4.

Model	GAN-OPC				LithoBench (MetalSet)				LithoBench (ViaSet)				MaskOpt (EBOPC)				MaskOpt (ILT)
Model	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	Shot
GAN-OPC	8690	13.8	9183	633	39512	3.9	42230	490	21219	0.3	705	148	66012	16.6	6732	111	65158	0.4	8749	376
DAMO	8472	14.7	8949	862	33704	3.8	42306	532	5984	8.7	9899	180	58661	15.3	7072	96	58972	0.4	9082	404
NeuralILT	8658	14.2	10336	1392	38065	4.1	43753	489	7104	8.6	9546	281	-	-	-	-	48643	5.0	6749	187
CFNO	9020	13.1	10297	461	43443	3.6	44738	350	20325	0.7	2609	76	-	-	-	-	61968	0.3	8613	291
MorphOPC	8107	13.6	9013	509	31915	4.1	41300	499	4974	8.2	9549	274	53642	4.9	8455	108	46860	4.0	6971	215

Table 1. Comparison with learning-based models across OPC benchmarks.

ICCAD 2013 Benchmark (Pretrained on GAN-OPC)
Test	GAN-OPC				DAMO				NeuralILT				CFNO				MorphOPC
Test	$\ell_{2}$	EPE	PVB	shot	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	shot	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	Shot
1	70120	9	55466	137	67407	8	49841	184	67628	10	64104	404	69332	6	49298	135	55356	10	51836	126
2	47234	8	46367	114	46291	8	46435	138	45027	7	52834	303	50620	5	53432	110	42015	8	46407	120
3	103656	6	85025	202	109048	6	67882	262	134856	9	74962	469	127178	0	74429	193	94007	1	64462	174
4	30165	0	24118	50	28385	1	24195	54	33372	2	36731	177	34783	1	36912	47	24585	1	23587	41

Table 2. Test comparison on ICCAD 2013 contest benchmark.

Larger Design Benchmark (Pretrained on GAN-OPC)
Test	GAN-OPC				DAMO				NeuralILT				CFNO				MorphOPC
Test	$\ell_{2}$	EPE	PVB	shot	$\ell_{2}$	EPE	PVB	shot	$\ell_{2}$	EPE	PVB	shot	$\ell_{2}$	EPE	PVB	shot	$\ell_{2}$	EPE	PVB	shot
11	110163	18	106714	311	96853	15	104298	340	108584	20	112203	749	124190	13	111745	259	94579	13	109699	283
12	104544	13	104633	288	83858	11	99311	282	89455	12	109796	551	103606	9	123921	258	79698	12	107312	237
13	159272	17	132406	346	147885	15	125778	404	142771	17	135333	821	177046	11	141396	304	134747	12	138711	314
14	86750	4	81864	196	65697	3	80406	215	68567	5	92746	499	83450	3	104105	168	62043	5	81967	196

Table 3. Test comparison on larger designs.

Figure 4. Test result visualization. Rows correspond to ten test cases from (a) the ICCAD 2013 benchmark, and (b) the MaskOpt edge-based OPC set: from top to bottom, each row corresponds to tiles of different standard cells, including AOI21_X2, BUF_X16, OAI221_X2, OR4_X2, BUF_X32, NAND3_X4, NOR3_X4, AND3_X1, CLKBUF_X1, and OR3_X1.

Figure 5. Average running time on ICCAD 2013 benchmark.

Ablation Experiment	GAN-OPC					ICCAD 2013 Benchmark
Ablation Experiment	MSE	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	Shot
MorphOPC	0.0046	8107	13.6	9013	509	42377	2.3	44555	119.7
C1. MorphBasic ✗	0.0047	8163	13.9	9176	514	47969	2.4	45484	126.1
C2. MultiScaleMorph ✗	0.0052	8404	13.9	9233	528	47651	2.3	50271	121.0
C3. MorphBasic,MultiScaleMorph ✗	0.0056	8679	14.7	10571	678	47304	2.7	43679	151.2

Table 4. Ablation Results.

MorphOPC Scale Factor	GAN-OPC					ICCAD 2013
MorphOPC Scale Factor	MSE	$\ell_{2}$	EPE	PVB	Shot	$\ell_{2}$	EPE	PVB	Shot
$s=4$	0.0049	8410	14.4	9312	506	44251	2.3	44554	123.3
$s=8$	0.0046	8107	13.6	9013	509	42377	2.3	44555	119.7
$s=16$	0.0052	7877	14.4	9385	530	44161	1.7	47761	113.7
$s=32$	0.0068	8833	14.0	9234	753	53634	1.9	44442	97.8

Table 5. Impact of scale factor on model performance.

Model	MultiILT					CurvyILT
Model	$\ell_{2}$	EPE	PVB	Shot	Slowdown	$\ell_{2}$	EPE	PVB	Shot	Speedup
GAN-OPC	29239	3.6	44501	527	2.04x	27865	3.6	42657	526	3.97%
DAMO	29165	3.6	44423	531	2.00x	27753	3.6	42654	526	4.29%
NeuralILT	28927	3.6	44666	507	2.00x	27685	3.6	42919	516	4.44%
CFNO	29266	3.6	44696	490	1.99×	27813	3.6	42582	492	4.21%
MorphOPC	28902	3.6	44309	527	1.98×	27501	3.6	42545	522	4.52%

Table 6. Initialize optimization-based OPC with model-generated mask on ICCAD 2013 benchmark.

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In semiconductor manufacturing, lithography projects circuit layouts onto silicon wafers through an optical mask. As circuit features shrink below the wavelength of light, optical diffraction causes the printed patterns to deviate from their intended layouts. Inverse Lithography Technology (ILT) addresses this challenge by generating optimized masks that enhance the fidelity of pattern transfer onto wafers. While ILT resembles an image synthesis task, its reliance on explicit physical metrics for mask evaluation limits the applicability of existing generative models. We introduce LithoGRPO, an ILT framework that integrates the flow-matching paradigm with GRPO-based reinforcement learning (RL) fine-tuning, enabling efficient exploration of diverse masks for a given target layout. Unlike purely generative or optimization-based approaches, RL in LithoGRPO exploits the explicitly defined, physics-based reward function of ILT, enabling optimization under complex, process-aware constraints. To the best of our knowledge, this is the first framework that unifies flow matching and RL for mask optimization. To improve RL sampling efficiency, we propose a fast shot-counting algorithm for manufacturability evaluation, achieving over 130x speedup while preserving the mask ranking of the traditional shot-count metric. Extensive experiments demonstrate that LithoGRPO achieves state-of-the-art performance over both optimization-based and learning-based methods, while maintaining efficient mask generation.

Abstract

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