H-Function Assist Feature Placement for Photomask Image Quality
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Solution Overview
Problem
Conventional methods for arranging assist features on masks in semiconductor fabrication are time-consuming and inefficient, often failing to optimize exposure and depth of focus due to the microscopic size of features and complex patterns, leading to reduced exposure latitude and depth of focus.
Innovation Solution
A method using an h-function to determine the optimal position of assist features based on their contribution to image intensity, involving the calculation of h(ξ-x) to maximize image intensity and apply optical proximity correction, ensuring precise placement and performance of mask patterns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If assist features are arranged by trial and error based on engineer's ability, then the arrangement can be made, but a large amount of time is required and optimal positions cannot be determined systematically
Solution Approach 1:
The patent replaces the manual trial-and-error mechanical process of arranging assist features with an automated computational system. The h-function calculation method uses mathematical optimization algorithms to automatically determine optimal assist feature positions, eliminating the need for engineer's manual trial and error arrangements and significantly reducing the time required while improving positioning precision.
Solution Approach 2:
The system enables self-service by allowing the h-function calculation method to automatically determine optimal assist feature positions without requiring engineer's expertise or manual intervention. The computational algorithm independently performs the optimization task, making the process self-sufficient and eliminating dependency on human skill and time investment.
2Illumination intensity
If assist features are arranged to increase image intensity, then depth of focus and exposure latitude can be increased, but the microscopic size of main features makes it difficult for light to pass through holes or lines on the mask
Solution Approach 1:
The h-function serves as an intermediary mathematical tool that bridges the conflict between increasing image intensity and maintaining light transmission. By calculating the contribution of each potential assist feature position to the image intensity, the h-function enables systematic optimization of assist feature placement to maximize illumination intensity while accounting for the microscopic constraints of the main features and light transmission requirements.
Solution Approach 2:
The patent applies parameter changes by systematically varying the position parameters of assist features based on h-function calculations. This allows optimization of the assist feature positions to achieve maximum image intensity enhancement while maintaining compatibility with the microscopic dimensions and light transmission requirements of the mask features.
3Adaptability or versatility
If various patterns are present on the mask, then the mask can represent complex circuits, but stable generation of assist features cannot be guaranteed
Solution Approach 1:
The patent applies segmentation by calculating h-functions for different pattern regions separately and independently. This allows the systematic determination of optimal assist feature positions for each local pattern while maintaining overall consistency. The segmented approach ensures stable assist feature generation across various complex patterns by treating each region according to its specific characteristics.
Solution Approach 2:
The h-function calculation method provides universality by serving as a single systematic approach that works for all types of mask patterns. This universal method guarantees stable assist feature generation across diverse and complex circuit patterns, eliminating the instability that occurs with conventional approaches when dealing with pattern variety.
Data Source
AI summary
In positioning assist features on a photomask pattern to improve the image quality of the main features, the method includes deriving an h-function in a first process which represents a contribution of an assist feature with respect to image intensity at a main feature. In a continuation of the method, the position of the assist features are determined in a second process using the h-function derived in the first step. The assist features are then formed on the mask at the positions indicated. Also included is a computer readable medium having instructions for performing the h-function calculations, and the mask apparatus itself with both main and assist features positioned according to the h-function.