Stochastic Error Modeling for Mask Process Variability
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional simulations in semiconductor manufacturing, particularly in photolithography processes, fail to accurately model random and non-uniform mask errors, leading to inaccuracies in pattern formation and device performance.
Innovation Solution
The implementation of stochastic error modeling, which applies probability distributions to simulate mask process errors, generating multiple mask layouts that account for random and non-uniform variations, thereby improving the accuracy of photolithography process simulations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional deterministic simulation methods are used for photolithography processes, then computational simplicity is maintained, but manufacturing precision and reliability of pattern formation deteriorate due to inability to account for random mask errors
Solution Approach 1:
The simulation approach is segmented into two distinct components: a deterministic component that handles the ideal mask pattern formation, and a stochastic component that separately models random mask errors using probability distributions. This segmentation allows each component to be optimized independently while combining their effects to achieve comprehensive accuracy.
Solution Approach 2:
A stochastic error model acts as an intermediary between the deterministic simulation and the actual physical process variations. This intermediary layer introduces controlled random variations based on measured probability distributions, bridging the gap between idealized simulations and real-world manufacturing variability.
2Reliability
If stochastic error modeling is implemented to account for random mask errors, then manufacturing precision and reliability improve, but computational complexity and processing time increase
Solution Approach 1:
Probability distributions of mask errors are determined and characterized in advance through preliminary measurements and data collection. These pre-characterized distributions are then reused in subsequent simulations, avoiding the need to generate and analyze error data during each simulation run, thus reducing processing time.
Solution Approach 2:
Instead of performing computationally intensive physical measurements for each simulation scenario, the invention creates virtual copies of mask error patterns by sampling from measured probability distributions. These synthetic error patterns replicate real-world variability without requiring repeated physical experiments or measurements.
3Manufacturing precision
If multiple mask layouts are generated using probability distributions, then manufacturing precision and critical dimension uniformity improve, but device complexity and data processing requirements worsen
Solution Approach 1:
The stochastic error model applies different probability distributions to different regions and features of the mask pattern based on their specific characteristics. Rather than applying a uniform error model across the entire mask, the approach tailors the error characteristics to local features, improving accuracy while managing computational load through selective detailed modeling.
Data Source
AI summary
Systems and methods are disclosed for a stochastic model of mask process variability of a photolithography process, such as for semiconductor manufacturing. In one embodiment, a stochastic error model may be based on a probability distribution of mask process error. The stochastic error model may generate a plurality of mask layouts having stochastic errors, such as random and non-uniform variations of contacts. In other embodiments, the stochastic model may be applied to critical dimension uniformity (CDU) optimization or design rule (DR) sophistication.