Curvature-Aware Etch Bias Simulation Model
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Solution Overview
Problem
Current etching simulation models in computational lithography do not account for the influence of in-plane curvatures of contours in a wafer pattern on etch bias, leading to inaccuracies in predicting etch effects and optimizing patterning processes.
Innovation Solution
A simulation model that correlates etch biases with curvatures of contours, using multi-dimensional algorithms including non-linear, linear, or quadratic functions, to determine etch biases based on contour slopes, maxima, minima, and derivatives, and incorporates these correlations to enhance the accuracy of patterning processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional etching simulation models are used that do not account for contour curvature, then the model complexity remains low, but the manufacturing precision of etch bias prediction deteriorates
Solution Approach 1:
The patent introduces curvature as a new parameter in the etching simulation model. The model now considers the curvature of contours at different locations on the substrate, transforming the simulation from a flat-plane assumption to a curvature-aware model. This parameter change enables accurate prediction of etch bias variations caused by contour curvature while maintaining computational feasibility through efficient algorithms.
Solution Approach 2:
The substrate surface is divided into multiple discrete locations, and the curvature is calculated separately for each location. This segmentation approach allows the model to handle complex varying curvatures across the substrate by treating each point independently, reducing the overall computational complexity while improving prediction accuracy at each specific location.
2Manufacturing precision
If curvature effects are incorporated into the simulation model, then the manufacturing precision of patterning processes improves, but the device complexity increases
Solution Approach 1:
The patent replaces complex physical etching simulations with a computational model that uses mathematical curvature calculations. Instead of simulating the actual etching physics in detail, the model uses curvature parameters derived from the pattern geometry to predict etch bias, substituting mechanical/physical simulation with mathematical computation that is more efficient and easier to implement.
Solution Approach 2:
The model transforms the patterning process simulation by incorporating curvature as a key parameter. By calculating curvature at different substrate locations and using these curvature values to determine etch bias, the model achieves higher patterning accuracy without requiring complex multi-physics simulations, thus improving precision while controlling complexity.
3Productivity
If curvature-based etch bias prediction is implemented, then the productivity of patterning process optimization improves, but the measurement precision requirements increase
Solution Approach 1:
The curvature of contours is calculated in advance before the etching process simulation. By pre-computing curvature values at all substrate locations based on the input pattern geometry, the model eliminates the need for repeated curvature calculations during iterative optimization, thereby improving productivity while requiring accurate initial contour measurements.
Solution Approach 2:
The patent uses the input pattern geometry as a template to calculate curvature distributions. By copying the pattern information and deriving curvature from this geometric representation, the model reduces measurement requirements to the initial pattern definition, avoiding the need for high-precision measurements during the actual etching process.
Data Source
AI summary
Etch bias is determined based on a curvature of a contour in a substrate pattern. The etch bias is configured to be used to enhance an accuracy of a semiconductor patterning process relative to prior patterning processes. In some embodiments, a representation of the substrate pattern is received, which includes the contour in the substrate pattern. The curvature of the contour of the substrate pattern is determined and inputted to a simulation model. The simulation model includes a correlation between etch biases and curvatures of contours. The etch bias for the contour in the substrate pattern is outputted by the simulation model based on the curvature.