# A Hierarchical Inverse Lithography Method Considering the Optimization and Manufacturability Limit by Gradient Descent

## TL;DR

This paper introduces a new inverse lithography method that improves optimization efficiency and avoids over-optimization issues in complex pattern layouts.

## Contribution

A resolution layering method and corner-rounding-inspired strategy are proposed to enhance GD-based ILT optimization.

## Key findings

- The proposed method improves optimization efficiency in inverse lithography.
- It effectively avoids over-optimization in complex pattern layouts.
- Numerical experiments confirm its superiority over existing methods.

## Abstract

Inverse lithography technology (ILT) based on the gradient descent (GD) algorithm, which is a classical local optimal method, can effectively improve the lithographic imaging fidelity. However, due to the low-pass filtering effect of the lithography imaging system, GD, although able to converge quickly, is prone to fall into the local optimum for the information in the corner region of complex patterns. Considering the high-frequency information of the corner region during the optimization process, this paper proposes a resolution layering method to improve the efficiency of GD-based ILT algorithms. A corner-rounding-inspired target retargeting strategy is used to compensate for the over-optimization defect of GD for inversely optimizing the complex pattern layout. Furthermore, for ensuring the manufacturability of masks, differentiable top-hat and bottom-hat operations are employed to improve the optimization efficiency of the proposed method. To confirm the superiority of the proposed method, multiple optimization methods of ILT were compared. Numerical experiments show that the proposed method has higher optimization efficiency and effectively avoids the over-optimization.