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ILILT: Implicit Learning of Inverse Lithography Technologies

Haoyu Yang, Haoxing Ren

TL;DR

ILILT introduces an implicit-layer learning framework for inverse lithography that grounds mask optimization in lithography physics through a lithography estimator. By formulating ILT as a fixed-point, weight-tied process and training over intermediate optimization states, ILILT achieves fast, high-quality mask generation that can outperform traditional numerical ILT solvers and prior ML methods. The approach demonstrates strong generalization, a clear speedup, and the ability to act as a practical solver in design workflows, with insights into unrolling depth and mask priors. This work potentially transforms AI-assisted design by directly embedding physical lithography constraints into the learning loop, reducing reliance on expensive simulations while preserving manufacturability. The empirical results on LithoBench show notable improvements in edge placement error and competitive processing throughput, indicating substantial practical impact for manufacturing-ready mask optimization.

Abstract

Lithography, transferring chip design masks to the silicon wafer, is the most important phase in modern semiconductor manufacturing flow. Due to the limitations of lithography systems, Extensive design optimizations are required to tackle the design and silicon mismatch. Inverse lithography technology (ILT) is one of the promising solutions to perform pre-fabrication optimization, termed mask optimization. Because of mask optimization problems' constrained non-convexity, numerical ILT solvers rely heavily on good initialization to avoid getting stuck on sub-optimal solutions. Machine learning (ML) techniques are hence proposed to generate mask initialization for ILT solvers with one-shot inference, targeting faster and better convergence during ILT. This paper addresses the question of \textit{whether ML models can directly generate high-quality optimized masks without engaging ILT solvers in the loop}. We propose an implicit learning ILT framework: ILILT, which leverages the implicit layer learning method and lithography-conditioned inputs to ground the model. Trained to understand the ILT optimization procedure, ILILT can outperform the state-of-the-art machine learning solutions, significantly improving efficiency and quality.

ILILT: Implicit Learning of Inverse Lithography Technologies

TL;DR

ILILT introduces an implicit-layer learning framework for inverse lithography that grounds mask optimization in lithography physics through a lithography estimator. By formulating ILT as a fixed-point, weight-tied process and training over intermediate optimization states, ILILT achieves fast, high-quality mask generation that can outperform traditional numerical ILT solvers and prior ML methods. The approach demonstrates strong generalization, a clear speedup, and the ability to act as a practical solver in design workflows, with insights into unrolling depth and mask priors. This work potentially transforms AI-assisted design by directly embedding physical lithography constraints into the learning loop, reducing reliance on expensive simulations while preserving manufacturability. The empirical results on LithoBench show notable improvements in edge placement error and competitive processing throughput, indicating substantial practical impact for manufacturing-ready mask optimization.

Abstract

Lithography, transferring chip design masks to the silicon wafer, is the most important phase in modern semiconductor manufacturing flow. Due to the limitations of lithography systems, Extensive design optimizations are required to tackle the design and silicon mismatch. Inverse lithography technology (ILT) is one of the promising solutions to perform pre-fabrication optimization, termed mask optimization. Because of mask optimization problems' constrained non-convexity, numerical ILT solvers rely heavily on good initialization to avoid getting stuck on sub-optimal solutions. Machine learning (ML) techniques are hence proposed to generate mask initialization for ILT solvers with one-shot inference, targeting faster and better convergence during ILT. This paper addresses the question of \textit{whether ML models can directly generate high-quality optimized masks without engaging ILT solvers in the loop}. We propose an implicit learning ILT framework: ILILT, which leverages the implicit layer learning method and lithography-conditioned inputs to ground the model. Trained to understand the ILT optimization procedure, ILILT can outperform the state-of-the-art machine learning solutions, significantly improving efficiency and quality.
Paper Structure (29 sections, 18 equations, 10 figures, 2 tables)

This paper contains 29 sections, 18 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. ILT Solver
  4. Implicit Layers
  5. Neural Networks for ML-based Computational Lithography
  6. The ILILT Framework
  7. ILT Layer
  8. Lithography Estimation
  9. Training
  10. Discussion
  11. Relations to ML-Aided Solutions
  12. Relations to Implicit Layer Learning
  13. Relations to Learning-to-Optimize
  14. Practical Usage Scenario
  15. Experiments
  16. ...and 14 more sections

Figures (10)

  • Figure 1: Limitations of lithography system requires design optimization to be correctly fabricated on the silicon wafer.
  • Figure 2: Working scheme of ILT solvers. (a) Standard ILT solver that iteratively updates the mask from design till convergence. (b) Common ML approach that uses ML to produce an initial mask followed by standard ILT procedure. (c) The ILILT that uses ML to imitate the standard ILT procedure.
  • Figure 3: Data example from LithoBench lithobench. (a) Design image contains the patterns of original circuit devices or connectivity; (b) Mask image is the optimized design that is manufacturing-friendly; (c) Wafer image is the patterns on silicon given the mask image.
  • Figure 4: Lithography edge placement error and process variations. Smaller EPE and PVB area indicates better optimization QoR.
  • Figure 5: Visualization of the optimization trajectory beyond the maximum unrolling depth. We use the model trained with unrolling step T=4, and mask stays stable after the 4th step with only minor tuning. (a)--(h) correspond to the generated masks generated from time stamps 1--8. (i)--(p) are the lithography simulated wafer image with their corresponding EPE violation count.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Definition 2.1: Implicit Layer
  • Definition 2.2: Fixed-Point Layer
  • Definition 4.1: EPE ViolationOPC-ICCAD2013-Banerjee
  • Definition 4.2: PVB AreaOPC-ICCAD2013-Banerjee