Electromagnetic Modeling of Finite Structures
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing electromagnetic modeling methods, such as rigorous coupled-wave analysis (RCWA), assume infinite periodic structures and infinite illuminating beams, requiring multiple simulations for each angle of incidence, making them impractical for fast inspection in high-volume semiconductor manufacturing and unable to accurately model non-periodic structures and realistic illumination.
Innovation Solution
The method involves computing background and scattered electric or magnetic fields using a scattered field formulation, allowing for the modeling of finite structures and finite illumination, enabling simulation of multiple angles of incidence in one simulation, and improving computational speed and precision by using spatial domain methods and deformed mesh techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If RCWA is used to solve light scattering problems, then spectral information can be obtained, but multiple simulations are required for each angle of incidence, making the method impractical for fast inspection
Solution Approach 1:
The patent segments the electromagnetic field into background fields and scattered fields. The background fields are computed once for all angles of incidence, and the scattered fields are computed by combining these background fields with different illumination angles through field superposition. This segmentation eliminates the need for multiple separate simulations for each angle of incidence.
Solution Approach 2:
The patent performs preliminary computation of background fields in advance, before the actual measurement or inspection. These pre-computed background fields are then reused for multiple angles of incidence by simply combining them with different illumination conditions, significantly reducing the total computational time required.
2Ease of manufacture
If RCWA assumes infinite periodic structures, then calculations are simplified, but non-periodic structures and realistic illumination cannot be accurately modeled
Solution Approach 1:
The patent separates the structure into a periodic background (which can be handled by RCWA) and a finite scattering object (which is modeled using spatial domain methods). This allows the benefits of RCWA for the periodic background while accurately modeling the finite non-periodic structure.
Solution Approach 2:
The patent introduces background fields as an intermediary that represents the infinite periodic structure and illumination, which then interact with the finite scattering object. This intermediary approach allows modeling of both infinite background conditions and finite target structures simultaneously.
3Measurement precision
If RCWA uses Fourier-space methods, then periodic structures can be modeled, but spatial domain effects and realistic illumination are not captured
Solution Approach 1:
The patent segments the modeling approach by using Fourier-space RCWA for the background periodic structure and spatial domain finite difference methods for the finite scattering object. This hybrid approach captures both periodic structure effects and spatial domain illumination effects.
Solution Approach 2:
The patent changes the mathematical domain from Fourier-space to spatial domain for the scattering object computation. By using spatial domain methods, the patent can accurately model realistic illumination patterns and spatial variations that cannot be captured in Fourier-space alone.
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
This approach significantly accelerates computational speed while achieving higher precision, enabling the modeling of non-periodic structures, realistic illumination, and improving accuracy for targets with metals or high-K materials, and allows for the simulation of roughness effects and multiple angles of incidence in a single simulation.
Implementation Method 1
computing scattered electric or magnetic fields from the diffracting structure using a scattered field formulation based on the computed background fields
Data Source
AI summary
Electromagnetic modeling of finite structures and finite illumination for metrology and inspection are described herein. In one embodiment, a method for evaluating a diffracting structure involves providing a model of the diffracting structure. The method involves computing background electric or magnetic fields of an environment of the diffracting structure. The method involves computing scattered electric or magnetic fields from the diffracting structure using a scattered field formulation based on the computed background fields. The method further involves computing spectral information for the model of the diffracting structure based on the computed scattered fields, and comparing the computed spectral information for the model with measured spectral information for the diffracting structure. In response to a good model fit, the method involves determining a physical characteristic of the diffracting structure based on the model of the diffracting structure.