Spatial Harmonic Truncation for Multi-Period Metrology Models
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Solution Overview
Problem
Current metrology systems face significant computational challenges when measuring complex semiconductor structures with multiple periodicities, leading to increased computational effort and memory requirements, making it impractical to achieve accurate results in a reasonable time.
Innovation Solution
The method involves grouping Fourier spatial harmonics based on the multiple periodicity of the metrology target, selecting distinct truncation orders and spacings for each group, and using these harmonics for regression and library generation to reduce computational effort and memory requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a single high truncation order is used to accurately represent all periodicities in complex semiconductor structures, then measurement accuracy is improved, but computational effort and memory requirements increase significantly
Solution Approach 1:
The patent segments the spatial harmonics into multiple groups based on their spatial frequencies, where each group corresponds to a specific periodicity component of the semiconductor structure. This segmentation allows different truncation orders to be applied to different groups, avoiding the need to use a single high truncation order for all harmonics, thereby reducing computational effort while maintaining measurement accuracy.
Solution Approach 2:
The patent applies local quality by assigning different truncation orders to different groups of spatial harmonics based on their specific requirements. High-frequency harmonics that require higher accuracy for representing fine structural details are assigned higher truncation orders, while low-frequency harmonics are assigned lower truncation orders. This localized optimization reduces overall computational complexity while preserving measurement precision where it is most needed.
2Measurement precision
If more spatial harmonics are included in the Fourier expansion, then solution accuracy is improved, but computational time increases
Solution Approach 1:
The patent applies partial action by selectively including only the necessary number of spatial harmonics in the Fourier expansion for each periodicity component. Instead of using an excessive number of harmonics uniformly across all components, the method determines the appropriate truncation order for each group of harmonics based on the specific accuracy requirements and spatial frequency characteristics, thereby reducing computational time while maintaining solution accuracy.
3Adaptability or versatility
If measurements are performed over large ranges of machine parameters simultaneously, then measurement comprehensiveness is improved, but measurement time and computation time increase significantly
Solution Approach 1:
The patent segments the parameter space and measurement process into multiple independent analyses, each handling a specific periodicity component with its own optimized truncation order. This segmentation allows the measurement system to process different parameter ranges more efficiently and can enable parallel processing of different periodicity components, thereby improving productivity while maintaining measurement comprehensiveness.
Data Source
AI summary
Methods and systems for solving measurement models of complex device structures with reduced computational effort and memory requirements are presented. The computational efficiency of electromagnetic simulation algorithms based on truncated spatial harmonic series is improved for periodic targets that exhibit a fundamental spatial period and one or more approximate periods that are integer fractions of the fundamental spatial period. Spatial harmonics are classified according to each distinct period of the target exhibiting multiple periodicity. A distinct truncation order is selected for each group of spatial harmonics. This approach produces optimal, sparse truncation order sampling patterns, and ensures that only harmonics with significant contributions to the approximation of the target are selected for computation. Metrology systems employing these techniques are configured to measure process parameters and structural and material characteristics associated with different semiconductor fabrication processes.