SOCS Decomposition for 3D Mask Image Intensity
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Solution Overview
Problem
Conventional photolithographic simulation tools using binary mask models inaccurately predict image intensity due to simplistic assumptions, leading to errors in resolution enhancement techniques (RETs) for complex 3D mask structures, especially under off-axis illumination, and are computationally intensive for full chip designs.
Innovation Solution
The method employs the Sum Of Coherent Systems (SOCS) algorithm to decompose features into 2D areas and edges within a window of relevance, using pre-calculated lookup tables to estimate image intensity under various illumination and coherency conditions, improving accuracy without significant increases in processing time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional binary mask models are used for simulation, then processing time is reduced, but image intensity prediction accuracy deteriorates
Solution Approach 1:
The patent segments the mask structure into distinct 3D geometric components (opaque regions, phase shifter regions, undercuts) and models light interaction separately for each segment. This allows accurate prediction of image intensity while maintaining computational efficiency by avoiding full-wave electromagnetic simulation of the entire complex mask structure.
Solution Approach 2:
The patent applies different optical models and parameters to different local regions of the mask based on their specific geometric characteristics. For example, separate models are used for opaque chromium regions versus phase shifter regions, and further refinements are applied to regions with undercuts. This localized modeling approach improves accuracy where it matters most while keeping overall computation manageable.
2Device complexity
If simplified binary mask models are used, then computational complexity is reduced, but prediction accuracy for 3D mask structures deteriorates
Solution Approach 1:
The mask is divided into discrete geometric segments (top surface regions, undercut regions, phase shifter regions) that can be modeled independently. This segmentation reduces computational complexity by breaking down the complex 3D electromagnetic problem into simpler, separable calculations while still capturing the essential physics of light-matter interaction for each region type.
Solution Approach 2:
The patent introduces additional geometric parameters (undercut depth, phase shifter thickness, material refractive indices) to the simulation model to accurately represent 3D mask structures. By incorporating these parameters into an otherwise computationally efficient framework, the model achieves high prediction accuracy for complex mask geometries without requiring full-wave electromagnetic simulation.
3Measurement precision
If full electromagnetic simulation is used for accurate image intensity prediction, then prediction accuracy improves, but processing time increases significantly
Solution Approach 1:
Rather than performing full electromagnetic simulation of the entire mask, the patent segments the problem into geometric region identification followed by analytical light interaction calculations for each region. This approach achieves comparable accuracy to full electromagnetic simulation but with dramatically reduced computational time by exploiting the piecewise nature of mask geometries.
Solution Approach 2:
The patent performs preliminary geometric analysis to identify and classify different mask regions (opaque, phase shifter, undercut) before conducting the actual image intensity calculation. This preliminary segmentation allows subsequent calculations to use optimized, simplified models appropriate for each region type, avoiding the computational overhead of general-purpose electromagnetic simulation.
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
This approach provides a more accurate and efficient calculation of image intensity for 3D mask features, reducing errors in RET applications and enabling faster processing times, essential for real-time OPC and other RET enhancements in photolithography.
Implementation Method 1
The method employs the Sum Of Coherent Systems (SOCS) algorithm to decompose features into 2D areas and edges within a window of relevance, using pre-calculated lookup tables to estimate image intensity under various illumination and coherency conditions
Implementation Method 2
In a conventional image intensity model, the light passing through various portions of the mask is modeled as a binary process with 100% light transmission occurring in transparent areas 60 on the mask and 0% transmission occurring in opaque areas 62 of the mask
Implementation Method 3
The difference in refractive index between the glass mask substrate and air provides a phase shift when apertures of different topography are used. When this phase-shift is 180 degrees, destructive interference occurs between light passing through the two apertures
Implementation Method 4
When off-axis illumination is used, additional scattering of light occurs from the edges of the etched apertures. This ultimately reduces the intensity of the light in the image formed from the phase shifted aperture
Data Source
AI summary
A system for estimating image intensity within a window area of a wafer using a SOCS decomposition to determine the horizontal and vertical edge fragments that correspond to objects within the window area. Results of the decomposition are used to access lookup tables that store data related to the contribution of the edge fragment to the image intensity. Each lookup table stores data that are computed under a different illumination and feature fabrication or placement conditions.