Multiple patterning lithography (MPL) has been widely used to improve lithography resolution in advanced nodes, but it faces cost limits as feature sizes shrink. Directed self-assembly (DSA) offers a cost-effective complement, extending the resolution of optical lithography to sub-10 nm and beyond. Integrating DSA into MPL (DSA-MP) further enhances the resolution of contact/via patterning. Nevertheless, growing design complexity exposes the limits of existing decomposition methods, which struggle to balance solution quality and runtime, and neglect edge-to-edge spacing constraints of DSA templates, compromising manufacturability. To address these issues, we introduce a new conflict graph model capturing the previously overlooked constraints and develop a local refinement strategy powered by the graph neural network, enabling efficient and scalable layout decomposition. Experiments demonstrate that our method achieves higher solution quality with faster convergence than state-of-the-art methods, while maintaining robustness across layout scales, design styles, technology nodes, and varying mask counts.
Figures & tables
Figure 1. (a) Traditional flow: solve from scratch until optimal or timeout. (b) Leveraging features from the initial solving phase, our flow predicts vias for mask reassignment. The solver reassigns masks only for these vias, keeping all others fixed, significantly speeding up convergence.
Figure 2. (a) DSA process flow. (b) Feasible templates: by adjusting template size, vias with different pitches can be fabricated, but the grouping range is limited by the natural pitch L0 of the BCP. Moreover, a minimum edge-to-edge spacing between templates is required to ensure stable patterning.
Figure 3. (a) Original layout. (b) Decomposition with triple patterning. (c) Decomposition with DSA-MP (The red solid line shows the lithography simulation result from S-litho). (d) Another decomposition with DSA-MP.
Figure 4. Transforming an ILP instance to a bipartite graph.
Figure 5. (a) Our graph model. It unifies lithography spacing and template-related conflicts as edge-to-edge constraints between templates. Each via can be manufactured by a single-hole template, while vias connected by a two-hole template edge may alternatively use the two-hole template. Template conflict hyperedges represent all possible template conflicts. (b) An example of a feasible mask and template assignment.
Figure 6. Illustration of three types of edge-to-edge template spacing conflicts, each with a representative ci highlighted by the black dashed arrow. (a) SC : taking ci=(a,b) as an example, a conflict between two single-hole templates. (b) STC : taking ci=(a,t1) as an example, a conflict between single-hole template a and two-hole template t1 . (c) TTC : taking ci=(t1,t2) as an example, a conflict between two-hole templates t1 and t2 .
Figure 7. Our proposed framework. (A) Synthetic layouts are generated based on design rules extracted from the ASAP7 PDK. A time-limited ILP solver produces an initial solution, and a constraint on the count of via changes is added to identify the minimal set of vias requiring reassignment, forming the Vias-to-Refine dataset. (B) The ILP formulation is represented as a bipartite graph, and solver-derived features initialize a GNN trained on the dataset from (A) to predict vias requiring reassignment. (C) For a test layout, a time-limited ILP solver provides an initial solution. Based on GNN-predicted probabilities, a subset of vias is sampled for reassignment, while others are fixed, and only the selected vias are re-optimized.
Benchmark
Original
EILP ( Lin and Jiang, 2019 )
DLXplus ( Lin and Jiang, 2019 )
Ours
via
edge
cn
tn
cost
time (s)
cn
tn
cost
time (s)
cn
tn
cost
time (s)
test1
3977
7140
103
137
104.37
268.63
261
128
262.28
104.44
103
145
104.45
105.94
test2
3807
6570
91
117
92.17
6655.68
220
98
220.98
85.18
91
120
92.20
50.09
test3
3795
6170
81
99
81.99
446.88
195
79
195.79
80.31
81
102
82.02
31.90
test4
12025
19882
265
314
268.14
11528.07
542
114
243.14
612.33
265
324
268.24
193.88
test5
5180
8587
127
110
128.10
76.65
265
112
266.12
189.71
127
113
128.13
84.02
Table 1. Comparison results of DSA with TPL on 7 nm synthetic layouts.
Benchmark
Original
EILP ( Lin and Jiang, 2019 )
DLXplus ( Lin and Jiang, 2019 )
Ours
via
edge
cn
tn
cost
time (s)
cn
tn
cost
time (s)
cn
tn
cost
time (s)
BOOM_test1
15608
24758
273
210
275.10
634.57
900
774
907.74
706.67
273
439
277.39
121.29
BOOM_test2
16729
26325
430
209
432.09
1551.12
1133
1003
1143.03
1012.96
432
598
437.98
96.59
BOOM_test3
11586
18492
266
116
267.16
305.98
747
522
752.22
107.73
268
360
271.60
58.88
BOOM_test4
31486
50113
918
377
921.77
4920.61
2177
1899
2195.99
2051.60
922
938
931.38
330.97
BOOM_test5
13540
21320
285
156
286.56
1176.25
881
782
888.82
538.01
285
427
289.27
76.72
Table 2. Comparison results of DSA with TPL on 7 nm BOOM core layouts
Benchmark
Original
EILP ( Lin and Jiang, 2019 )
DLXplus ( Lin and Jiang, 2019 )
Ours
via
edge
cn
tn
cost
time (s)
cn
tn
cost
time (s)
cn
tn
cost
time (s)
N5_test1
4328
8244
27
288
29.88
299.25
115
255
117.55
50.26
27
294
29.94
44.51
N5_test2
7829
14772
40
540
45.40
2035.96
181
515
186.15
409.49
41
545
46.45
55.33
N5_test3
7006
12840
40
442
44.42
1230.44
151
435
155.35
196.12
40
453
44.53
58.89
N5_test4
10268
19226
55
741
62.41
541.88
247
703
254.03
549.43
55
749
62.49
88.20
N5_test5
6671
12262
25
436
29.36
653.43
134
408
138.08
147.88
25
441
29.41
48.95
Table 3. Comparison results of DSA with QPL on 5 nm industrial layouts.
Benchmark
Original
EILP ( Lin and Jiang, 2019 )
DLXplus ( Lin and Jiang, 2019 )
Ours
via
edge
cn
tn
cost
time (s)
cn
tn
cost
time (s)
cn
tn
cost
time (s)
N5_test_11
5551
11120
TLE
TLE
TLE
TLE
161
403
165.03
122.05
34
526
39.26
57.51
test11
116215
206000
TLE
TLE
TLE
TLE
TLE
TLE
TLE
TLE
3622
3895
3660.95
4636.34
test12
206659
366628
TLE
TLE
TLE
TLE
TLE
TLE
TLE
TLE
6287
6421
6351.21
17265.78
BOOM_test11
221696
352602
TLE
TLE
TLE
TLE
TLE
TLE
TLE
TLE
6054
5572
6109.72
5856.67
BOOM_test12
667477
1056475
TLE
TLE
TLE
TLE
TLE
TLE
TLE
TLE
18315
18787
18502.87
49369.75
Table 4. Cases where some algorithms exceed the 20-hour time limit (“TLE”).
Figure 8. Ablation study on solver-derived features.
Training Data
cn
tn
cost
time (s)
the BOOM core layouts
44.4
556.7
49.967
97.218
Synthetic layouts
39.5
527.8
44.778
103.085
Table 5. GNN performance on 5 nm industrial layouts with different training sets.
Figure 9. Manufacturability comparison among no DSA (MPL only), prior conflict graph model, and our proposed conflict graph model.
Figure 10. Post-OPC lithography simulation results. Gray rectangles denote targets and colored contours represent simulated printed patterns on different masks. (a) Results obtained using the prior conflict graph model. (b) Results obtained using our proposed conflict graph model.
Semiconductor manufacturing uses process engineering, metrology, and automation to make chips reliably, improve yield, and meet tight device requirements.
As semiconductor manufacturing advances toward sub-2nm nodes, local place-and-route (P&R) design-rule violation (DRV) fixing is increasingly limited by complex rule interactions, dense multi-layer routing geometries, and foundry-specific constraints. While Large Language Models (LLMs) have recently demonstrated strong capabilities in EDA scripting and documentation, their application to visual layout understanding remains largely unexplored: diagnosing DRC violations from layout imagery demands precise geometric reasoning and foundry-specific rule knowledge absent from general-purpose VLM training. We propose SCALE, a framework with a self-supervised layout-generation stage for local DRV fixing at advanced nodes. Multi-layer layout geometry is serialized into structured text, and a fine-tuned language model learns to reconstruct randomly masked polygons from surrounding BEOL context alone without violation labels. At inference, natural-language rule constraints and high-temperature sampling steer generation toward diverse, violation-prone layout variants validated by an industrial signoff DRC checker, producing DRC-annotated layout--violation pairs used to fine-tune a domain-adapted DRC-VLM. This VLM provides rule-aware geometric guidance for local DRV repair, boosting state-of-the-art agents' solve rates by +12--25% (up to 97%) on 100 real sub-2nm cases spanning enclosure, spacing, width, and color-spacing violations.
Macro placement is a pivotal stage in VLSI physical design, fundamentally determining the overall chip performance. Recent data-driven placement methods have demonstrated significant potential, yet they often struggle to handle sequential dependencies and to balance topological connectivity with physical constraints. To bridge this gap, we propose MacroDiff+, a physics-guided geometric diffusion framework. Specifically, we design a dual-domain denoising architecture that couples topological connectivity encoded by heterogeneous GNNs with global geometric context modeled by a Transformer. Furthermore, we introduce Physics-Guided Sampling, an inference strategy that actively steers the generation using explicit gradients to ensure both statistical plausibility and physical validity. On the ISPD2005 MMS benchmarks, MacroDiff+ outperforms state-of-the-art baselines with a 6.1-6.2% reduction in wirelength. Notably, it exhibits superior stability and scalability on large-scale designs where prior methods fail to converge. The source code is available at https://github.com/jhy00n/MacroDiff-plus.
Jongho Yoon, Jinsung Jeon, Seokhyeong Kang
1POSTECH Institute of Artificial Intelligence · 2KAIST InnoCORE LLM · 3Seoul National University +1
We propose using Vision-Language Models (VLMs) for macro placement in chip floorplanning, a complex optimization task that has recently shown promising advancements through machine learning methods. Because human designers rely heavily on spatial reasoning to arrange components on the chip canvas, we hypothesize that VLMs with strong spatial reasoning capabilities can effectively complement existing placement algorithms. We introduce VeoPlace (Visual Evolutionary Optimization Placement), a novel framework that uses a VLM, without any fine-tuning, to guide the actions of a base placer by constraining it to subregions of the chip canvas. The VLM proposals are iteratively optimized through an evolutionary search strategy with respect to resulting placement quality. Using global half-perimeter wirelength (gHPWL) after standard-cell placement and legalization as the evaluation metric, VeoPlace boosts ChiPFormer performance on 9 of 10 benchmarks with peak reductions exceeding 32%. We further demonstrate that VeoPlace generalizes to analytical placers, improving DREAMPlace on all 8 evaluated Superblue benchmarks with gains up to 4.4%. Our approach opens new possibilities for electronic design automation tools that leverage foundation models to solve complex physical design problems.
Ikechukwu Uchendu, Swati Goel, Karly Hou +5
Harvard University, Cambridge, MA, USA · Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA, USA · Google DeepMind