3D Mask Simulation Filters for Fabrication-Aware Lithography
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Solution Overview
Problem
Lithography simulations for semiconductor wafer manufacturing are computationally intensive and less accurate due to the lack of consideration for mask fabrication effects, leading to inefficiencies in predicting electromagnetic field scattering characteristics.
Innovation Solution
Utilize modified three-dimensional (M3D) filters that account for mask fabrication effects by parameterizing them with spatial shifts and additive/multiplicative constants, calculated from wafer measurements, and stored as lookup tables for efficient use in simulations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If rigorous three-dimensional simulations are used to compute mask functions, then accuracy of electromagnetic field scattering characteristics is improved, but computational time and complexity increase significantly
Solution Approach 1:
The patent pre-computes three-dimensional mask filters during an offline preparation phase and stores them in a library. During actual lithography simulations, these pre-computed filters are reused through convolution operations, eliminating the need to perform intensive three-dimensional electromagnetic simulations repeatedly. This preliminary action resolves the contradiction by shifting computational burden from runtime to preparation time.
Solution Approach 2:
The patent creates simplified two-dimensional representations (copies) of the three-dimensional mask structure by convolving the mask layout with pre-computed three-dimensional filters. These two-dimensional mask function images serve as accurate approximations that can be used in standard lithography simulation workflows without requiring full three-dimensional electromagnetic simulations, thus reducing computational time while maintaining accuracy.
2Measurement precision
If mask fabrication effects are incorporated into three-dimensional mask models, then prediction accuracy of mask function is improved, but device complexity and computational load increase
Solution Approach 1:
The patent incorporates mask fabrication effects by modifying the three-dimensional mask filters with fabrication-specific parameters such as sidewall angles, thickness variations, and material properties. These parameterized filters are pre-computed and stored in the filter library, allowing accurate representation of fabrication effects without increasing runtime computational complexity. The complexity is managed by embedding fabrication parameters in the offline filter generation phase.
3Measurement precision
If full-chip or large-scale computational lithography applications are performed with accurate three-dimensional mask modeling, then prediction accuracy is improved, but computational resources and time requirements become prohibitive
Solution Approach 1:
The patent pre-computes and stores three-dimensional mask filters in a reusable library before performing full-chip lithography simulations. This allows large-scale applications to efficiently reuse pre-computed filters through convolution operations, making accurate three-dimensional mask modeling computationally feasible for entire chips rather than just small test patterns.
Solution Approach 2:
The patent generates two-dimensional mask function images by convolving the mask layout with pre-computed three-dimensional filters. These two-dimensional representations can be processed using standard lithography simulation tools, enabling full-chip simulations with accurate three-dimensional effects without requiring prohibitively expensive three-dimensional electromagnetic solvers for every simulation step.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Improves simulation accuracy and reduces computational burden, enabling faster and more precise predictions of lithography outcomes while maintaining efficiency in both machine learning and graphics processing unit frameworks.
Implementation Method 1
Mask function (MF) contributions from individual feature images are calculated by convolving the feature image with a corresponding three-dimensional mask (M3D) filter. The M3D filters represent an electromagnetic scattering effect of that feature image.
Implementation Method 2
The illumination pattern that exposes resist on a wafer depends on the geometric layout of the lithographic mask and the source illumination, among other factors. Simulation of the lithographic process depends on an accurate prediction of the electromagnetic field produced by the source illumination incident on the lithographic mask.
Implementation Method 3
The M3D filters represent an electromagnetic scattering effect of that feature image.
Data Source
AI summary
Feature images representing a layout geometry of a lithographic mask are received. Mask function (MF) contributions from individual feature images are calculated by convolving the feature image with a corresponding three-dimensional mask (M3D) filter. The M3D filters represent an electromagnetic scattering effect of that feature image. At least one M3D filter also accounts for effects arising from a fabrication process for the lithographic mask.