Photomask Pattern Optimization Using Approximate Merit Functions
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Solution Overview
Problem
In photolithography processes, the increasing demand for feature density on semiconductor wafers leads to distortions and artifacts due to the wave nature of light, making it challenging to achieve optimal photomask patterns, especially when computing gradients and merit functions becomes computationally intensive.
Innovation Solution
The method involves representing photomask patterns using hierarchical polygon representations and functional representations, employing a slower, more accurate merit function and a faster, approximate one to optimize patterns, and dividing the patterns into blocks for parallel processing, allowing for efficient full-chip optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If gradient based optimization methods are used to find optimal photomask patterns, then manufacturing precision is improved, but computing time and complexity increase
Solution Approach 1:
The patent uses a simplified approximate merit function that is computationally inexpensive and can be evaluated quickly multiple times during optimization, replacing the need for expensive accurate merit function evaluations while still guiding the optimization toward the correct solution
Solution Approach 2:
The patent changes the parameter representation from polygonal coordinates to level set function values on a grid, enabling the use of gradient-based optimization methods that work more efficiently with this continuous representation, thereby reducing computational complexity
2Manufacturing precision
If accurate merit functions are used to evaluate photomask patterns, then manufacturing precision is improved, but productivity decreases due to time-intensive computation
Solution Approach 1:
The patent applies partial action by using the approximate merit function for the majority of optimization iterations and only using the accurate merit function selectively to verify convergence or for final validation, thus achieving good enough results with significantly reduced computation time
Solution Approach 2:
The patent introduces an intermediary approximate merit function that bridges between the simple fast evaluation and the complex accurate evaluation, providing a computationally efficient proxy that guides optimization while maintaining connection to the accurate metric through periodic comparisons
3Manufacturing precision
If gradient computation is performed for optimization, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent replaces the complex mechanical computation of gradients with respect to polygon parameters with a simpler field-based approach using level set functions, where gradients are computed with respect to function values on a grid, fundamentally simplifying the computational mechanics
4Manufacturing precision
If detailed polygonal representations are used for photomask patterns, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent transforms the parameter representation from discrete polygon vertex coordinates to continuous level set function values defined on a regular grid, fundamentally changing how the pattern is represented and enabling more efficient computation while maintaining manufacturing precision
Data Source
AI summary
Photomask patterns are represented using contours defined by mask functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks. An accurate, slower merit function may be used to determine adjustment parameters for a faster, approximate merit function. The faster merit function may be used for iteration and adjusted based on the adjustment parameters.