Photomask Data Synthesis via Smooth Curve Fitting
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Solution Overview
Problem
Existing methods for compensating photomask data in integrated circuit fabrication lead to segmentation and movement of edges, making the lithography target not lithography-friendly, and are counterproductive in representing the inverse etch correction, which results in suboptimal edge segments.
Innovation Solution
A method that synthesizes a photomask data set by fitting smooth curves to target polygons, moving etch target points based on an etch process model, and adjusting the lithography process model to minimize errors in image intensity and edge placement, using algorithms like Overmars-Welzl and Ghosh-Mount for visibility graphs and point-spread-functions for pattern density effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If multi-step process proximity correction (PPC) is used to compensate for etch and lithography distortions, then manufacturing precision is improved, but the lithography target becomes segmented and edge segments become suboptimal, worsening ease of manufacture
Solution Approach 1:
Instead of directly computing the inverse etch transformation TETCH^-1(PTARGET) which produces segmentation and suboptimal edges, the patent inverts the approach by forward-simulating the etch process multiple times with different mask patterns and using optimization to find the mask pattern that produces the desired target. This inversion transforms an ill-posed inverse problem into a well-posed optimization problem.
Solution Approach 2:
The patent creates multiple copies of the target pattern with slight variations and uses them as test patterns in the optimization process. By forward-simulating etch on these copied patterns and comparing results to the desired target, the method iteratively refines the mask pattern without directly computing problematic inverse transformations.
2Device complexity
If polygon-based representation is used for inverse etch correction, then computational simplicity is maintained, but edge segmentation occurs and lithography friendliness is lost, worsening manufacturing precision
Solution Approach 1:
The patent changes the representation parameters from simple polygon vertices to splines defined by control points and coefficients. This parameter transformation allows smooth, continuous edge representations that are lithography-friendly while maintaining computational tractability through the optimization framework. The spline parameters are optimized to minimize the difference between simulated and desired patterns.
3Device complexity
If inverse transformations are computed sequentially (tandem correction), then process decoupling is achieved, but cumulative errors increase and final pattern accuracy deteriorates, worsening manufacturing precision
Solution Approach 1:
The patent merges the lithography and etch correction steps into a unified optimization framework. Instead of sequentially applying TETCH^-1 then TLITHO^-1, the method simultaneously optimizes the mask pattern to account for both processes, using forward simulation of the complete process chain and gradient-based optimization to minimize cumulative errors.
Data Source
AI summary
A method for synthesizing a photomask data set from a given target layout, including the following steps: (a) providing a set of target polygons for the target layout; (b) fitting a smooth curve to a target polygon of the set of target polygons, the curve having a set of etch-target points; (c) moving the etch target points according to a model of an etch process to produce a set of lithography-target points; and (d) synthesizing a photomask data set based on a model of a lithography process and the set of lithography-target points.