Plasma Etching Simulation Solid Angle Flux Method
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Solution Overview
Problem
Current plasma etching simulation methods, such as the flux method, face challenges in accurately predicting the processing shape of high aspect ratio patterns due to increased calculation errors and load, and lack versatility in handling inequiaxial structures, while the Monte Carlo method is computationally intensive.
Innovation Solution
A simulation method that calculates a solid angle corresponding to a field-of-view region and uses a flux method with a function considering reaction probability to predict the incident radical amount, reducing calculation load and improving precision by accounting for multiple pseudo-reemissions and stagnation effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the flux method is used to calculate the indirect component, then the calculation cost is reduced, but the accuracy of predicting processing shape deteriorates for high aspect ratio patterns
Solution Approach 1:
The patent introduces a solid angle parameter (Ω) that represents the field-of-view region for plasma space viewing from an evaluation point. This parameter change enables the flux method to account for multiple pseudo-reemissions and stagnation effects, improving accuracy for high aspect ratio patterns while maintaining computational efficiency. The solid angle calculation replaces complex Monte Carlo simulations with a more efficient geometric approach.
2Device complexity
If the flux method assumes single reemission, then the calculation is simplified, but errors in indirect flux calculation increase for high aspect ratio patterns requiring multiple reemissions
Solution Approach 1:
The patent adds a solid angle dimension (Ω) to the flux calculation, transforming the traditional two-dimensional flux approach into a three-dimensional consideration that includes the field-of-view region. This dimensional extension allows the calculation to capture multiple reemission paths and stagnation effects without significantly increasing computational complexity, as the solid angle can be calculated using geometric relationships between surface elements.
3Ease of manufacture
If the flux method uses surface element information, then the calculation can be performed, but the calculation load becomes proportional to the square of the surface element, increasing rapidly with aspect ratio
Solution Approach 1:
The patent introduces a solid angle (Ω) as an intermediary parameter that mediates between the flux calculation and the surface element geometry. Instead of directly calculating flux based on complex surface element interactions (which would require O(N²) operations), the solid angle serves as a pre-calculable geometric factor that simplifies the flux computation to O(N) operations, significantly reducing the calculation load for high aspect ratio patterns.
4Ease of manufacture
If the flux method is applied to axisymmetric cylindrical shapes, then the calculation can be performed, but versatility is limited when target patterns have inequiaxial structures with different peripheral opening ratios
Solution Approach 1:
The patent makes the flux method universal by introducing a solid angle calculation that works for any pattern shape, not just axisymmetric cylindrical structures. The solid angle (Ω) is calculated based on the general geometric relationship between the evaluation point and the plasma space viewing region, making the method applicable to inequiaxial structures and various pattern configurations. This universal approach allows the same calculation framework to handle different pattern types without requiring shape-specific modifications.
Data Source
AI summary
A simulation method includes acquiring a processing condition for performing predetermined processing on a processing target with use of plasma, calculating a solid angle corresponding to a field-of-view region through which plasma space is viewable from a predetermined evaluation point in the predetermined evaluation point on a surface of the processing target based on the processing condition, and calculating an incident radical amount entering the evaluation point by a flux method with use of a function which takes a reaction probability between the solid angle and the evaluation point of a radical entering the evaluation point as an argument.