Lithography Model Transfer Function for Resist Thickness Prediction
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Solution Overview
Problem
Current photolithography process models, whether physical or black box, face challenges in accurately predicting resist exposure and development due to complexity and computational intensity, with existing models either lacking accuracy or requiring extensive resources, and failing to effectively account for various process parameters.
Innovation Solution
A lithography model that uses a transfer function to relate exposure energy dose to remaining resist thickness, incorporating process variables such as aerial image intensity, acid diffusion, and bake conditions, allowing for more accurate simulation while reducing computational requirements by being based on physical processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If physical models are used to simulate photolithography processes, then interpolation and extrapolation accuracy is improved, but computational complexity increases
Solution Approach 1:
The photolithography process model is segmented into distinct physical stages: optical proximity effect calculation, acid diffusion simulation, and resist development modeling. Each stage is handled by specialized sub-models that can be independently optimized and computed, reducing overall computational complexity while maintaining accuracy.
Solution Approach 2:
The patent replaces complex mechanical/physical simulation systems with mathematically equivalent but computationally more efficient formulations. Specifically, partial differential equations describing acid diffusion are transformed into analytically solvable forms or simplified numerical schemes that preserve physical accuracy while reducing computational burden.
2Adaptability or versatility
If black box models are used to accommodate various process parameters, then adaptability is improved, but interpolation and extrapolation accuracy deteriorates
Solution Approach 1:
The model incorporates multiple process parameters (exposure dose, focus offset, resist thickness, bake conditions) as explicit variables that can be adjusted independently. By formulating the model with these parameters as controllable inputs rather than fixed constants, the system achieves adaptability while maintaining physical-based accuracy for interpolation and extrapolation.
Solution Approach 2:
The patent develops a universal photolithography model framework that can handle multiple process conditions and parameter variations within a single unified formulation. This multi-functional model accommodates different resist types, exposure wavelengths, and process conditions without requiring separate black-box models for each scenario.
3Adaptability or versatility
If variable threshold models are used to account for process parameter variations, then adaptability is improved, but computational intensity increases
Solution Approach 1:
The model pre-calculates and stores lookup tables for acid diffusion profiles and resist development characteristics under various conditions. During actual simulation, these pre-computed data structures are queried and combined with current process parameters, avoiding repeated intensive numerical computations while still accounting for parameter variations.
Solution Approach 2:
The patent implements a variable threshold model that selectively applies full computational complexity only where process parameter variations significantly impact results. In regions where parameters have minimal effect, simplified calculations are used, reducing overall computational intensity while maintaining necessary accuracy.
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 provides accurate interpolation and extrapolation results, capable of simulating three-dimensional resist profiles, enhancing the prediction of resist exposure and development processes, and improving the manufacturability of IC designs with reduced computational burden.
Implementation Method 1
Photolithography is the process of transferring patterns of geometric shapes on a mask to a thin layer of photosensitive material (resist) covering the surface of a semiconductor wafer
Implementation Method 2
The resist component includes, among others, acid diffusion
Data Source
AI summary
A lithography model uses a transfer function to map exposure energy dose to the thickness of remaining photoresist after development; while allowing the flexibility to account for other physical processes. In one approach, the model is generated by fitting empirical data. The model may be used in conjunction with an aerial image to obtain a three-dimensional profile of the remaining photoresist thickness after the development process. The lithography model is generally compact, yet capable of taking into account various physical processes associated with the photoresist exposure and/or development process for more accurate simulation.