Resist Deformation Prediction via Fluid Dynamics Simulation
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Solution Overview
Problem
Current techniques for predicting pattern deformation in resist layers during semiconductor manufacturing are inadequate and slow, failing to accurately assess complex shape changes due to intrafluid forces like surface tension, which affects downstream processes such as material deposition and etching.
Innovation Solution
A fluid dynamics model based on Navier-Stokes equations is used to simulate the deformation of resist patterns, accounting for intrafluid forces and predicting deformation with high accuracy by iterating through updates of model parameters until criteria are met.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current prediction techniques are used, then the prediction process is simple, but the prediction accuracy is low and the prediction speed is slow
Solution Approach 1:
The patent replaces traditional mechanical/mathematical deformation models with a fluid dynamics model that treats the resist layer as a viscous fluid. This substitution enables accurate prediction of complex pattern deformations by applying Navier-Stokes equations and surface tension calculations, resolving the contradiction between prediction accuracy and computational complexity.
Solution Approach 2:
The patent changes the fundamental parameters of the prediction model by introducing fluid dynamic parameters (viscosity, surface tension coefficients) instead of traditional elastic or plastic deformation parameters. This parameter transformation allows the model to accurately capture the behavior of resist materials during lithographic processing while maintaining computational efficiency through established fluid dynamics solvers.
2Measurement precision
If fluid dynamics model is used, then the prediction accuracy is high, but the model complexity increases
Solution Approach 1:
The patent replaces complex solid mechanics models with fluid dynamics models, leveraging the well-established mathematical framework of Navier-Stokes equations. This substitution simplifies the theoretical complexity while improving accuracy for resist material behavior, as fluid dynamics naturally captures the viscous and surface tension effects dominant in lithographic resist layers.
Solution Approach 2:
The patent applies a universal fluid dynamics framework that can handle various resist material properties and processing conditions through a single unified model. By using general fluid dynamic equations with adjustable parameters (viscosity, surface tension), the model achieves high prediction accuracy across different scenarios without requiring separate complex models for each case.
3Reliability
If traditional methods are used, then the process is fast, but the ability to account for intrafluid forces is insufficient
Solution Approach 1:
The patent substitutes traditional mechanical deformation theories with fluid dynamics models that inherently account for intrafluid forces such as surface tension and viscosity. This substitution provides reliable prediction of pattern deformations caused by these forces while utilizing efficient computational fluid dynamics algorithms to maintain acceptable prediction speeds for industrial applications.
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 model effectively predicts resist pattern deformation, reducing errors in critical dimension measurements and improving the accuracy of lithography processes by accounting for surface tension and other intrafluid forces, leading to better pattern formation and yield in semiconductor manufacturing.
Implementation Method 1
a fluid dynamics model based on Navier-Stokes equations is used to simulate the deformation of resist patterns, accounting for intrafluid forces like surface tension
Data Source
AI summary
A method involving obtaining a resist deformation model for simulating a deformation process of a pattern in resist, the resist deformation model being a fluid dynamics model configured to simulate an intrafluid force acting on the resist, performing, using the resist deformation model, a computer simulation of the deformation process to obtain a deformation of the developed resist pattern for an input pattern to the resist deformation model, and producing electronic data representing the deformation of the developed resist pattern for the input pattern.