Wafer Shape Simulation Using Local Aperture Ratios
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Solution Overview
Problem
Existing shape simulation methods for semiconductor production face inaccuracies due to dimensional discrepancies in etched patterns, despite similar wafer aperture ratios and effective solid angles, indicating the need to consider additional factors for improved prediction accuracy.
Innovation Solution
A shape simulation apparatus and program that compute incident flux based on solid angles, wafer aperture ratios, and semilocal aperture ratios, allowing for time-evolution of wafer surface coordinates to enhance three-dimensional surface shape prediction, incorporating a flux computation block and shape computation block to improve simulation accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional shape simulation methods are used considering only wafer aperture ratio and effective solid angle, then the simulation process remains simple, but the prediction accuracy of etched pattern dimensions deteriorates due to dimensional discrepancies
Solution Approach 1:
The patent segments the aperture ratio concept into three distinct levels: wafer aperture ratio (global), local aperture ratio (regional), and effective solid angle (point-specific). This segmentation allows each level to capture different aspects of pattern geometry, thereby improving prediction accuracy without requiring a complete overhaul of the simulation framework
Solution Approach 2:
The patent applies local quality by introducing local aperture ratio calculations for specific regions containing calculation points, rather than using a single global aperture ratio. This allows the simulation to account for spatial variations in pattern density and geometry, improving dimensional prediction accuracy while maintaining computational feasibility through localized analysis
2Manufacturing precision
If additional factors such as local aperture ratio are incorporated into the simulation, then the prediction accuracy improves, but the computational complexity and processing time increase
Solution Approach 1:
The patent performs preliminary calculations of solid angles and aperture ratios for discrete calculation points before the main simulation process. By pre-computing these geometric parameters and storing them in data structures, the simulation avoids repeated calculations during the etching process simulation, thereby reducing overall computation time while maintaining high dimensional accuracy
Solution Approach 2:
The patent uses a discrete set of calculation points distributed across the wafer surface rather than continuous analysis. This partial action approach provides sufficient accuracy for manufacturing predictions while significantly reducing computational burden compared to full continuous field analysis
Data Source
AI summary
Disclosed herein is a shape simulation apparatus including: a flux computation block configured to compute the flux of particles incident on the surface of a wafer covered with a mask; and a shape computation block configured to compute a surface shape of the wafer by allowing the coordinates of a plurality of calculation points established on the surface of the wafer to be time-evolved based on the incident flux computed.