Lithography Stochastic Modeling for Failure Probability Prediction
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Solution Overview
Problem
Lithographic processes, particularly EUV lithography, face significant challenges due to stochastic randomness, leading to defects such as line edge roughness and critical dimension non-uniformity, which can result in the failure of electronic circuits. Existing methods like Monte Carlo simulations are computationally expensive and inefficient in addressing these issues.
Innovation Solution
A stochastic model is employed to analyze and mitigate stochastic randomness by generating a probability distribution of deprotection concentration, allowing for the optimization of light exposure and resist processes to reduce failure probabilities. This model can include continuous random field, Gaussian random field, or multivariate normal distribution models, and is used to modify the lithographic process parameters to improve yield.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo simulations are used to analyze stochastic randomness in lithographic processes, then the accuracy of predicting stochastic failures (such as line edge roughness and critical dimension non-uniformity) is improved, but the computational cost and runtime increase significantly
Solution Approach 1:
The patent replaces expensive, computationally intensive Monte Carlo simulations with a cheaper analytical model based on probability distribution functions. This analytical approach provides sufficient accuracy for predicting stochastic failures without the prohibitive computational cost of running numerous Monte Carlo simulation trials
Solution Approach 2:
The patent substitutes the computational mechanics of Monte Carlo simulations with an analytical mathematical model. Instead of using repeated numerical simulations to estimate failure probabilities, the invention uses closed-form probability distribution functions that directly calculate the likelihood of stochastic defects, thereby eliminating the need for extensive computational resources
2Reliability
If Monte Carlo simulations are performed with multiple trials to estimate failure probability, then the reliability of the prediction is improved, but the computational resources and complexity required increase
Solution Approach 1:
The patent replaces complex, resource-intensive Monte Carlo simulation infrastructure with a simple analytical model that computes failure probabilities using probability distribution functions. This approach maintains prediction reliability while eliminating the need for complex simulation frameworks and multiple trial runs
Solution Approach 2:
The patent uses analytical probability distribution functions that replicate the statistical behavior observed in Monte Carlo simulations without requiring actual simulation trials. The analytical model captures the essential stochastic characteristics of the lithographic process, providing reliable failure probability estimates through mathematical formulation rather than computational experimentation
3Measurement precision
If experimental measurements with multiple instances are conducted to calculate failure frequency, then the accuracy of stochastic effect characterization is improved, but the time and resource consumption increase
Solution Approach 1:
The patent performs preliminary characterization of stochastic effects through analytical modeling rather than requiring extensive experimental measurements. By establishing probability distribution functions based on fundamental process parameters, the method enables accurate prediction of failure frequencies without the need for numerous physical test runs
Solution Approach 2:
The patent substitutes physical experimental measurements with analytical calculations. Instead of conducting repeated experiments to characterize stochastic variability, the invention uses mathematical models that compute failure probabilities directly from process parameters, thereby maintaining measurement accuracy while dramatically improving productivity
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
The stochastic model significantly reduces the computational burden and runtime required for analyzing stochastic failures, enabling efficient optimization of lithographic processes, thereby enhancing the reliability and yield of electronic circuits by accurately predicting and mitigating stochastic defects.
Implementation Method 1
model stochastic randomness in one or both of exposure or resist process
Implementation Method 2
The polymer contains certain functional groups which get cleaved due to chemical reactions caused by exposure to light (deprotection)
Data Source
AI summary
A method and system for calculating probability of success or failure for a lithographic process due to stochastic variations of the lithographic process are disclosed. Lithography is a process that uses light to transfer a geometric pattern from a photomask, based on a layout design, to a resist on a substrate. The lithographic process is subject to random stochastic phenomena, such as photon shot noise and stochastic phenomena in the resist process and resist development, with the resulting stochastic randomness potentially becoming a major challenge. The stochastic phenomena are modeled using a stochastic model, such as a random field model, that models stochastic randomness the exposure and resist process. The stochastic model inputs light exposure and resist parameters and definitions of success of success or failure as to the lithographic process, and outputs a probability distribution function of deprotection concentration indicative of success or failure probability of the lithographic process. In turn, the probability distribution function may be used to modify one or both of the light exposure and resist parameters in order to reduce the effect of stochastic randomness on the lithographic process.